Salehi, Saeed On rudimentarity, primitive recursivity and representability. (English) Zbl 07250409 Rep. Math. Logic 55, 73-85 (2020). MSC: 03F40 03D20 03F30 PDF BibTeX XML Cite \textit{S. Salehi}, Rep. Math. Logic 55, 73--85 (2020; Zbl 07250409) Full Text: DOI
Leivant, Daniel Finitism, imperative programs and primitive recursion. (English) Zbl 07197408 Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2020, Deerfield Beach, FL, USA, January 04–07, 2020. Proceedings. Cham: Springer (ISBN 978-3-030-36754-1/pbk; 978-3-030-36755-8/ebook). Lecture Notes in Computer Science 11972, 98-110 (2020). MSC: 03B70 PDF BibTeX XML Cite \textit{D. Leivant}, Lect. Notes Comput. Sci. 11972, 98--110 (2020; Zbl 07197408) Full Text: DOI
Ardeshir, Mohammad; Khaniki, Erfan; Shahriari, Mohsen A counterexample to polynomially bounded realizability of basic arithmetic. (English) Zbl 07120751 Notre Dame J. Formal Logic 60, No. 3, 481-489 (2019). MSC: 03F30 03F50 PDF BibTeX XML Cite \textit{M. Ardeshir} et al., Notre Dame J. Formal Logic 60, No. 3, 481--489 (2019; Zbl 07120751) Full Text: DOI Euclid
Razon, Aharon Primitive recursive decidability for large rings of algebraic integers. (English) Zbl 1409.12003 Albanian J. Math. 13, No. 1, 3-93 (2019). MSC: 12L05 12E30 03C60 PDF BibTeX XML Cite \textit{A. Razon}, Albanian J. Math. 13, No. 1, 3--93 (2019; Zbl 1409.12003) Full Text: Link
Cordón-Franco, Andrés; Lara-Martín, F. Félix Local induction and provably total computable functions. (English) Zbl 1316.03037 Ann. Pure Appl. Logic 165, No. 9, 1429-1444 (2014). Reviewer: Roman Murawski (Poznań) MSC: 03F30 03D20 03C62 PDF BibTeX XML Cite \textit{A. Cordón-Franco} and \textit{F. F. Lara-Martín}, Ann. Pure Appl. Logic 165, No. 9, 1429--1444 (2014; Zbl 1316.03037) Full Text: DOI
Aschieri, Federico A constructive analysis of learning in Peano arithmetic. (English) Zbl 1257.03083 Ann. Pure Appl. Logic 163, No. 11, 1448-1470 (2012). Reviewer: G. E. Mints (Stanford) MSC: 03F03 03F30 03F55 PDF BibTeX XML Cite \textit{F. Aschieri}, Ann. Pure Appl. Logic 163, No. 11, 1448--1470 (2012; Zbl 1257.03083) Full Text: DOI
Ye, Feng Strict finitism and the logic of mathematical applications. (English) Zbl 1279.03006 Synthese Library 355. Dordrecht: Springer (ISBN 978-94-007-1346-8/hbk; 978-94-007-3631-3/pbk; 978-94-007-1347-5/ebook). xii, 272 p. (2011). Reviewer: Roman Murawski (Poznań) MSC: 03-02 00A30 03A05 03A10 PDF BibTeX XML Cite \textit{F. Ye}, Strict finitism and the logic of mathematical applications. Dordrecht: Springer (2011; Zbl 1279.03006) Full Text: DOI
Beklemishev, Lev D. On the Craig interpolation and the fixed point properties for GLP. (English) Zbl 1229.03049 Feferman, Solomon (ed.) et al., Proofs, categories and computations. Essays in honor of Grigori Mints. With the collaboration of Vladik Kreinovich, Vladimir Lifschitz, and Ruy de Queiroz. London: College Publications (ISBN 978-1-84890-012-7/pbk). Tributes 13, 49-60 (2010). Reviewer: Mladen Vuković (Zagreb) MSC: 03F45 03C40 PDF BibTeX XML Cite \textit{L. D. Beklemishev}, Tributes 13, 49--60 (2010; Zbl 1229.03049)
Burgess, John P. On the outside looking in: a caution about conservativeness. (English) Zbl 1241.03003 Feferman, Solomon (ed.) et al., Kurt Gödel. Essays for his centennial. Cambridge: Cambridge University Press; Ithaca, NY: Association for Symbolic Logic (ASL) (ISBN 978-0-521-11514-8/hbk). Lecture Notes in Logic 33, 128-141 (2010). Reviewer: Liesbeth De Mol (Gent) MSC: 03A05 03-03 01A60 03B30 PDF BibTeX XML Cite \textit{J. P. Burgess}, Lect. Notes Log. 33, 128--141 (2010; Zbl 1241.03003)
Marchenkov, S. S. On the complexity of the \({\mathcal E}^2\) Grzegorczyk class. (English. Russian original) Zbl 1217.03027 Discrete Math. Appl. 20, No. 1, 61-73 (2010); translation from Diskretn. Mat. 22, No. 1, 5-16 (2010). Reviewer: Marat M. Arslanov (Kazan) MSC: 03D20 03D15 PDF BibTeX XML Cite \textit{S. S. Marchenkov}, Discrete Math. Appl. 20, No. 1, 61--73 (2010; Zbl 1217.03027); translation from Diskretn. Mat. 22, No. 1, 5--16 (2010) Full Text: DOI
Bílková, Marta; de Jongh, Dick; Joosten, Joost J. Interpretability in PRA. (English) Zbl 1184.03011 Ann. Pure Appl. Logic 161, No. 2, 128-138 (2009). Reviewer: Mladen Vuković (Zagreb) MSC: 03B45 03F30 03F45 PDF BibTeX XML Cite \textit{M. Bílková} et al., Ann. Pure Appl. Logic 161, No. 2, 128--138 (2009; Zbl 1184.03011) Full Text: DOI
Impens, Chris; Sanders, Sam Saturation and \(\Sigma_2\)-transfer for ERNA. (English) Zbl 1184.03071 J. Symb. Log. 74, No. 3, 901-913 (2009). Reviewer: Emil Jeřábek (Praha) MSC: 03H05 03F30 PDF BibTeX XML Cite \textit{C. Impens} and \textit{S. Sanders}, J. Symb. Log. 74, No. 3, 901--913 (2009; Zbl 1184.03071) Full Text: DOI
Schirn, Matthias; Niebergall, Karl-Georg Finitism = PRA? On a thesis of W. W. Tait. (English) Zbl 1100.03008 Rep. Math. Logic 39, 3-24 (2005). Reviewer: Roman Murawski (Poznań) MSC: 03A05 03F30 PDF BibTeX XML Cite \textit{M. Schirn} and \textit{K.-G. Niebergall}, Rep. Math. Logic 39, 3--24 (2005; Zbl 1100.03008)
Salehi, Saeed Polynomially bounded recursive realizability. (English) Zbl 1097.03051 Notre Dame J. Formal Logic 46, No. 4, 407-417 (2005). Reviewer: Osamu Sonobe (Follonica) MSC: 03F30 03F50 PDF BibTeX XML Cite \textit{S. Salehi}, Notre Dame J. Formal Logic 46, No. 4, 407--417 (2005; Zbl 1097.03051) Full Text: DOI
Caldon, Patrick; Ignjatović, Aleksandar On mathematical intrumentalism. (English) Zbl 1089.03007 J. Symb. Log. 70, No. 3, 778-794 (2005). MSC: 03A05 03F30 03F35 00A30 PDF BibTeX XML Cite \textit{P. Caldon} and \textit{A. Ignjatović}, J. Symb. Log. 70, No. 3, 778--794 (2005; Zbl 1089.03007) Full Text: DOI
Ferreira, Fernando A simple proof of Parsons’ theorem. (English) Zbl 1095.03063 Notre Dame J. Formal Logic 46, No. 1, 83-91 (2005). MSC: 03F30 03D20 PDF BibTeX XML Cite \textit{F. Ferreira}, Notre Dame J. Formal Logic 46, No. 1, 83--91 (2005; Zbl 1095.03063) Full Text: DOI
Zaslavsky, I. D. On some generalizations of the primitive recursive arithmetic. (English) Zbl 1058.03064 Theor. Comput. Sci. 322, No. 1, 221-230 (2004). MSC: 03F30 03D20 68Q05 PDF BibTeX XML Cite \textit{I. D. Zaslavsky}, Theor. Comput. Sci. 322, No. 1, 221--230 (2004; Zbl 1058.03064) Full Text: DOI
Weiermann, Andreas An application of graphical enumeration to PA. (English) Zbl 1041.03045 J. Symb. Log. 68, No. 1, 5-16 (2003). Reviewer: Roman Murawski (Poznań) MSC: 03F30 PDF BibTeX XML Cite \textit{A. Weiermann}, J. Symb. Log. 68, No. 1, 5--16 (2003; Zbl 1041.03045) Full Text: DOI
Petersen, Uwe \(\mathbf L^i \mathbf D^Z_\lambda\) as a basis for PRA. (English) Zbl 1025.03059 Arch. Math. Logic 42, No. 7, 665-694 (2003). MSC: 03F30 03F05 03F52 PDF BibTeX XML Cite \textit{U. Petersen}, Arch. Math. Logic 42, No. 7, 665--694 (2003; Zbl 1025.03059) Full Text: DOI
Salehi, Saeed Decidable formulas of intuitionistic primitive recursive arithmetic. (English) Zbl 1027.03046 Rep. Math. Logic 36, 55-61 (2002). MSC: 03F30 03B25 03F55 PDF BibTeX XML Cite \textit{S. Salehi}, Rep. Math. Logic 36, 55--61 (2002; Zbl 1027.03046)
Weiermann, Andreas Slow versus fast growing. (English) Zbl 1024.03039 Synthese 133, No. 1-2, 13-29 (2002). Reviewer: Helmut Pfeiffer (Hannover) MSC: 03D20 03F15 03F35 PDF BibTeX XML Cite \textit{A. Weiermann}, Synthese 133, No. 1--2, 13--29 (2002; Zbl 1024.03039) Full Text: DOI
Kohlenbach, Ulrich On uniform weak König’s lemma. (English) Zbl 1001.03052 Ann. Pure Appl. Logic 114, No. 1-3, 103-116 (2002). Reviewer: Jeffry L.Hirst (Boone) MSC: 03F35 03F50 03F10 03F25 03D65 PDF BibTeX XML Cite \textit{U. Kohlenbach}, Ann. Pure Appl. Logic 114, No. 1--3, 103--116 (2002; Zbl 1001.03052) Full Text: DOI
Todorčević, Stevo Hierarchies of Ackermann, Baire and von Neumann. (English) Zbl 1003.03041 Proceedings of the 10th congress of Yugoslav mathematicians, Belgrade, Yugoslavia, January 21-24, 2001. Belgrade: University of Belgrade, Faculty of Mathematics. 11-20 (2001). Reviewer: Predrag Tanović (Beograd) MSC: 03D55 03-02 03D20 11B25 03E55 20F36 28A20 03F30 PDF BibTeX XML Cite \textit{S. Todorčević}, in: Proceedings of the 10th congress of Yugoslavian mathematicians, Belgrade, Yugoslavia, January 21--24, 2001. Belgrade: University of Belgrade, Faculty of Mathematics. 11--20 (2001; Zbl 1003.03041)
Kohlenbach, Ulrich Intuitionistic choice and restricted classical logic. (English) Zbl 0992.03072 Math. Log. Q. 47, No. 4, 455-460 (2001). MSC: 03F10 03F35 03F50 PDF BibTeX XML Cite \textit{U. Kohlenbach}, Math. Log. Q. 47, No. 4, 455--460 (2001; Zbl 0992.03072) Full Text: DOI
Sudac, O. The prime number theorem is PRA-provable. (English) Zbl 0974.03048 Theor. Comput. Sci. 257, No. 1-2, 185-239 (2001). MSC: 03F30 PDF BibTeX XML Cite \textit{O. Sudac}, Theor. Comput. Sci. 257, No. 1--2, 185--239 (2001; Zbl 0974.03048) Full Text: DOI
Michelbrink, Markus On the finite treatment of the proof theory of weak fragments of the set theory: \(\mathbf{KP} +\Pi_3\)-reflexion. (Zur endlichen Behandlung der Beweistheorie schwacher Fragmente der Mengenlehre: \(\mathbf{KP} +\Pi_3\)-Reflexion.) (German) Zbl 1070.03038 Hannover: Univ. Hannover, Fachbereich Mathematik und Informatik (Dissertation). 94 p. (2000). MSC: 03F15 03E70 03-02 03F03 03F05 03F07 03F25 03F35 03D20 PDF BibTeX XML Cite \textit{M. Michelbrink}, Zur endlichen Behandlung der Beweistheorie schwacher Fragmente der Mengenlehre: \(\mathbf{KP} +\Pi_3\)-Reflexion. Hannover: Univ. Hannover, Fachbereich Mathematik und Informatik (Dissertation) (2000; Zbl 1070.03038) Full Text: Link
Krivtsov, Victor N. A negationless interpretation of intuitionistic theories. (English) Zbl 0981.03062 Erkenntnis 53, No. 1-2, 155-172 (2000). Reviewer: Ulrich Kohlenbach (Aarhus) MSC: 03F50 03F55 03F25 PDF BibTeX XML Cite \textit{V. N. Krivtsov}, Erkenntnis 53, No. 1--2, 155--172 (2000; Zbl 0981.03062) Full Text: DOI
Kohlenbach, Ulrich Things that can and things that cannot be done in PRA. (English) Zbl 0958.03039 Ann. Pure Appl. Logic 102, No. 3, 223-245 (2000). Reviewer: Jeffry L.Hirst (Boone) MSC: 03F35 03D20 03F10 68Q15 PDF BibTeX XML Cite \textit{U. Kohlenbach}, Ann. Pure Appl. Logic 102, No. 3, 223--245 (2000; Zbl 0958.03039) Full Text: DOI
Beklemishev, L. Another pathological well-ordering. (English) Zbl 0943.03045 Buss, Samuel R. (ed.) et al., Logic colloquium ’98. Proceedings of the annual European summer meeting of the Association for Symbolic Logic, Prague, Czech Republic, August 9-15, 1998. Natick, MA: A K Peters, Ltd. Lect. Notes Log. 13, 105-108 (2000). MSC: 03F30 03F15 PDF BibTeX XML Cite \textit{L. Beklemishev}, Lect. Notes Log. 13, 105--108 (2000; Zbl 0943.03045)
Damnjanovic, Zlatan Strictly primitive recursive realizability. II: Completeness with respect to iterated reflection and a primitive recursive \(\omega\)-rule. (English) Zbl 0971.03060 Notre Dame J. Formal Logic 39, No. 3, 363-388 (1998). Reviewer: Roman Murawski (Poznań) MSC: 03F30 03F55 PDF BibTeX XML Cite \textit{Z. Damnjanovic}, Notre Dame J. Formal Logic 39, No. 3, 363--388 (1998; Zbl 0971.03060) Full Text: DOI
Weiermann, Andreas How is it that infinitary methods can be applied to finitary mathematics? Gödel’s \(T\): A case study. (English) Zbl 0928.03066 J. Symb. Log. 63, No. 4, 1348-1370 (1998). Reviewer: G.Mints (Stanford) MSC: 03F35 PDF BibTeX XML Cite \textit{A. Weiermann}, J. Symb. Log. 63, No. 4, 1348--1370 (1998; Zbl 0928.03066) Full Text: DOI
Parsons, Charles Finitism and intuitive knowledge. (English) Zbl 0918.03003 Schirn, Matthias (ed.), The philosophy of mathematics today. Papers from a conference, Munich, Germany, June 28–July 4, 1993. Oxford: Clarendon Press. 249-270 (1998). Reviewer: C.F.Kielkopf (Columbus/Ohio) MSC: 03A05 00A30 PDF BibTeX XML Cite \textit{C. Parsons}, in: The philosophy of mathematics today. Papers from a conference, Munich, Germany, June 28--July 4, 1993. Oxford: Clarendon Press. 249--270 (1998; Zbl 0918.03003)
Kunen, Kenneth Nonconstructive computational mathematics. (English) Zbl 0922.03076 J. Autom. Reasoning 21, No. 1, 69-97 (1998). Reviewer: M.Yasuhara (Princeton) MSC: 03F30 03B35 03D20 68T15 PDF BibTeX XML Cite \textit{K. Kunen}, J. Autom. Reasoning 21, No. 1, 69--97 (1998; Zbl 0922.03076) Full Text: DOI
Esbelin, Henri-Alex; More, Malika Rudimentary relations and primitive recursion: A toolbox. (English) Zbl 0896.03031 Theor. Comput. Sci. 193, No. 1-2, 129-148 (1998). MSC: 03D20 03F30 PDF BibTeX XML Cite \textit{H.-A. Esbelin} and \textit{M. More}, Theor. Comput. Sci. 193, No. 1--2, 129--148 (1998; Zbl 0896.03031) Full Text: DOI
Bellantoni, Stephen J. Ranking arithmetic proofs by implicit ramification. (English) Zbl 0890.03034 Beame, Paul W. (ed.) et al., Proof complexity and feasible arithmetics. Papers from the DIMACS workshop, Rutgers, NJ, USA, April 21–24, 1996. Providence, RI: American Mathematical Society. DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 39, 37-57 (1998). MSC: 03F30 03F20 68Q15 03D20 03F07 PDF BibTeX XML Cite \textit{S. J. Bellantoni}, DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 39, 37--57 (1998; Zbl 0890.03034)
Belyakin, N. V.; Odintsov, S. P. Infinite arithmetic formulas and the reflection principle. (English. Russian original) Zbl 0937.03066 Algebra Logika 36, No. 3, 245-258 (1997); translation in Algebra Logic 36, No. 3, 147-154 (1997). MSC: 03F30 PDF BibTeX XML Cite \textit{N. V. Belyakin} and \textit{S. P. Odintsov}, Algebra Logika 36, No. 3, 245--258 (1997; Zbl 0937.03066); translation in Algebra Logic 36, No. 3, 147--154 (1997)
Beklemishev, Lev D. Parameter free induction and reflection. (English) Zbl 0892.03023 Gottlob, Georg (ed.) et al., Computational logic and proof theory. 5th Kurt Gödel Colloquium, KGC ’97. Vienna, Austria. August 25–29, 1997. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1289, 103-113 (1997). Reviewer: M.Tetruašvili (Tbilisi) MSC: 03F30 03D20 PDF BibTeX XML Cite \textit{L. D. Beklemishev}, Lect. Notes Comput. Sci. 1289, 103--113 (1997; Zbl 0892.03023)
Dougherty, Randall; Jech, Thomas Finite left-distributive algebras and embedding algebras. (English) Zbl 0884.08006 Adv. Math. 130, No. 2, 201-241 (1997). Reviewer: S.Oates-Williams (St.Lucia) MSC: 08B20 08B25 03E55 20N02 PDF BibTeX XML Cite \textit{R. Dougherty} and \textit{T. Jech}, Adv. Math. 130, No. 2, 201--241 (1997; Zbl 0884.08006) Full Text: DOI arXiv
Kashima, Ryo; Yamaguchi, Takeshi On the difficulty of writing out formal proofs in arithmetic. (English) Zbl 0880.03031 Math. Log. Q. 43, No. 3, 328-332 (1997). Reviewer: R.Kossak (New York) MSC: 03F30 03D25 PDF BibTeX XML Cite \textit{R. Kashima} and \textit{T. Yamaguchi}, Math. Log. Q. 43, No. 3, 328--332 (1997; Zbl 0880.03031) Full Text: DOI
Dougherty, Randall; Jech, Thomas Left-distributive embedding algebras. (English) Zbl 0868.20052 Electron. Res. Announc. Am. Math. Soc. 3, 28-37 (1997). MSC: 20N02 03E55 08B20 03E35 PDF BibTeX XML Cite \textit{R. Dougherty} and \textit{T. Jech}, Electron. Res. Announc. Am. Math. Soc. 3, No. 4, 28--37 (1997; Zbl 0868.20052) Full Text: DOI EuDML
Wehmeier, Kai F. Fragments of HA based on \(\Sigma_ 1\)-induction. (English) Zbl 0886.03040 Arch. Math. Logic 37, No. 1, 37-49 (1997). Reviewer: K.F.Wehmeier (Münster) MSC: 03F30 03D20 PDF BibTeX XML Cite \textit{K. F. Wehmeier}, Arch. Math. Logic 37, No. 1, 37--49 (1997; Zbl 0886.03040) Full Text: DOI
Dougherty, Randall Critical points in an algebra of elementary embeddings. II. (English) Zbl 0856.03040 Hodges, Wilfrid (ed.) et al., Logic: from foundations to applications. European logic colloquium, Keele, UK, July 20–29, 1993. Oxford: Clarendon Press. 103-136 (1996). MSC: 03E55 PDF BibTeX XML Cite \textit{R. Dougherty}, in: Logic: from foundations to applications. European logic colloquium, Keele, UK, July 20--29, 1993. Oxford: Clarendon Press. 103--136 (1996; Zbl 0856.03040) Full Text: arXiv
Kotlarski, Henryk An addition to Rosser’s theorem. (English) Zbl 0848.03030 J. Symb. Log. 61, No. 1, 285-292 (1996). MSC: 03F30 PDF BibTeX XML Cite \textit{H. Kotlarski}, J. Symb. Log. 61, No. 1, 285--292 (1996; Zbl 0848.03030) Full Text: DOI
Zelmanov, E. More on Burnside’s problem. (English) Zbl 0849.20031 Duncan, Andrew J. (ed.) et al., Combinatorial and geometric group theory. Proceedings of a workshop held at Heriot-Watt University, Edinburgh, GB, spring of 1993. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 204, 314-321 (1995). Reviewer: E.Khukhro (Cardiff) MSC: 20F50 20D15 20D60 20F40 20E10 17B60 PDF BibTeX XML Cite \textit{E. Zelmanov}, Lond. Math. Soc. Lect. Note Ser. 204, 314--321 (1995; Zbl 0849.20031)
Kunen, Kenneth A Ramsey theorem in Boyer-Moore logic. (English) Zbl 0836.03031 J. Autom. Reasoning 15, No. 2, 217-235 (1995). MSC: 03F30 03-04 68T15 PDF BibTeX XML Cite \textit{K. Kunen}, J. Autom. Reasoning 15, No. 2, 217--235 (1995; Zbl 0836.03031) Full Text: DOI
Leivant, Daniel Ramified recurrence and computational complexity. I: Word recurrence and poly-time. (English) Zbl 0844.03024 Clote, Peter (ed.) et al., Feasible mathematics II. Based on a workshop, held at the Cornell University, Ithaca, NY, USA, May 28-30, 1992. Boston, MA: Birkhäuser. Prog. Comput. Sci. Appl. Log. 13, 320-343 (1995). Reviewer: P.van Emde Boas (Amsterdam) MSC: 03D20 03D15 03D10 68Q15 03F30 68Q25 PDF BibTeX XML Cite \textit{D. Leivant}, Prog. Comput. Sci. Appl. Log. 13, 320--343 (1995; Zbl 0844.03024)
Takeuti, Gaisi Grzegorcyk’s hierarchy and \(\text{Iep}\Sigma_ 1\). (English) Zbl 0816.03028 J. Symb. Log. 59, No. 4, 1274-1284 (1994). Reviewer: G.Mints (Stanford) MSC: 03F30 03F03 PDF BibTeX XML Cite \textit{G. Takeuti}, J. Symb. Log. 59, No. 4, 1274--1284 (1994; Zbl 0816.03028) Full Text: DOI
Damnjanovic, Zlatan Strictly primitive recursive realizability. I. (English) Zbl 0816.03029 J. Symb. Log. 59, No. 4, 1210-1227 (1994). Reviewer: R.Murawski (Poznań) MSC: 03F30 03F55 PDF BibTeX XML Cite \textit{Z. Damnjanovic}, J. Symb. Log. 59, No. 4, 1210--1227 (1994; Zbl 0816.03029) Full Text: DOI
Galvan, Sergio A note on the \(\omega\)-incompleteness formalization. (English) Zbl 0813.03039 Stud. Log. 53, No. 3, 389-396 (1994). Reviewer: F.G.Asenjo (Pittsburgh) MSC: 03F30 PDF BibTeX XML Cite \textit{S. Galvan}, Stud. Log. 53, No. 3, 389--396 (1994; Zbl 0813.03039) Full Text: DOI
Ignjatović, Aleksandar Hilbert’s program and the omega-rule. (English) Zbl 0820.03002 J. Symb. Log. 59, No. 1, 322-343 (1994). Reviewer: G.Kreisel (Oxford) MSC: 03A05 03-03 01A60 PDF BibTeX XML Cite \textit{A. Ignjatović}, J. Symb. Log. 59, No. 1, 322--343 (1994; Zbl 0820.03002) Full Text: DOI
Cook, Stephen; Urquhart, Alasdair Functional interpretations of feasibly constructive arithmetic. (English) Zbl 0780.03026 Ann. Pure Appl. Logic 63, No. 2, 103-200 (1993). Reviewer: G.Mints (Stanford) MSC: 03F30 03F50 03B40 03F03 68Q15 PDF BibTeX XML Cite \textit{S. Cook} and \textit{A. Urquhart}, Ann. Pure Appl. Logic 63, No. 2, 103--200 (1993; Zbl 0780.03026) Full Text: DOI
Kohlenbach, Ulrich Pointwise hereditary majorization and some applications. (English) Zbl 0729.03031 Arch. Math. Logic 31, No. 4, 227-242 (1992). Reviewer: U.Kohlenbach MSC: 03F30 PDF BibTeX XML Cite \textit{U. Kohlenbach}, Arch. Math. Logic 31, No. 4, 227--242 (1992; Zbl 0729.03031) Full Text: DOI
Gentilini, Paolo Provability logic in the Gentzen formulation of arithmetic. (English) Zbl 0794.03079 Z. Math. Logik Grundlagen Math. 38, No. 5-6, 535-550 (1992). Reviewer: P.Gentilini MSC: 03F30 03B45 03F03 03F05 PDF BibTeX XML Cite \textit{P. Gentilini}, Z. Math. Logik Grundlagen Math. 38, No. 5--6, 535--550 (1992; Zbl 0794.03079) Full Text: DOI
Feferman, Solomon Logics for termination and correctness of functional programs. II: Logics of strength PRA. (English) Zbl 0790.03029 Aczel, Peter (ed.) et al., Proof theory. A selection of papers from the Leeds proof theory programme, an international summer school and conference on proof theory, held at the Leeds University, UK, from July 24-August 2, 1990. Cambridge: Cambridge University Press. 197-225 (1992). Reviewer: R.S.Lubarsky (Lancaster) MSC: 03B70 68N01 03F30 68Q60 PDF BibTeX XML Cite \textit{S. Feferman}, in: Proof theory. A selection of papers from the Leeds proof theory programme, an international summer school and conference on proof theory, held at the Leeds University, UK, from July 24-August 2, 1990. Cambridge: Cambridge University Press. 197--225 (1992; Zbl 0790.03029)
Wainer, S. S.; Wallen, L. A. Basic proof theory. (English) Zbl 0793.03056 Aczel, Peter (ed.) et al., Proof theory. A selection of papers from the Leeds proof theory programme, an international summer school and conference on proof theory, held at the Leeds University, UK, from July 24-August 2, 1990. Cambridge: Cambridge University Press. 3-26 (1992). MSC: 03F03 03-01 03F05 03F30 PDF BibTeX XML Cite \textit{S. S. Wainer} and \textit{L. A. Wallen}, in: Proof theory. A selection of papers from the Leeds proof theory programme, an international summer school and conference on proof theory, held at the Leeds University, UK, from July 24-August 2, 1990. Cambridge: Cambridge University Press. 3--26 (1992; Zbl 0793.03056)
Fernando, T. A primitive recursive set theory and AFA: On the logical complexity of the largest bisimulation. (English) Zbl 0783.03031 Börger, Egon (ed.) et al., Computer science logic. 5th workshop, CSL ’91, Berne, Switzerland, October 7-11, 1991. Proceedings. Berlin etc.: Springer-Verlag. Lect. Notes Comput. Sci. 626, 96-110 (1992). Reviewer: N.Curteanu (Iaşi) MSC: 03F30 68Q10 68Q55 03C65 PDF BibTeX XML Cite \textit{T. Fernando}, Lect. Notes Comput. Sci. 626, 96--110 (1992; Zbl 0783.03031)
Feferman, Solomon Logics for termination and correctness of functional programs. (English) Zbl 0754.03018 Logic from computer science, Proc. Workshop, Berkeley/CA (USA) 1989, Publ., Math. Sci. Res. Inst. 21, 95-127 (1992). Reviewer: R.S.Lubarsky (Lancaster) MSC: 03B70 03F35 03F30 PDF BibTeX XML Cite \textit{S. Feferman}, in: Logic from computer science. Proceedings of a workshop, held November 13- 17, 1989, at the Mathematical Sciences Research Institute, Berkeley, CA, USA. New York etc.: Springer-Verlag. 95--127 (1992; Zbl 0754.03018)
Sieg, Wilfried Herbrand analyses. (English) Zbl 0722.03040 Arch. Math. Logic 30, No. 5-6, 409-441 (1991). Reviewer: M.Yasuhara (Princeton) MSC: 03F03 03F30 03F35 PDF BibTeX XML Cite \textit{W. Sieg}, Arch. Math. Logic 30, No. 5--6, 409--441 (1991; Zbl 0722.03040) Full Text: DOI
Yodaiken, Victor The algebraic feedback product of automata. A state machine based model of concurrent systems. (English) Zbl 0789.68101 Computer-aided verification ’90, Proc. 2nd DIMACS Workshop, New Brunswick/NJ (USA) 1990, DIMACS, Ser. Discret. Math. Theor. Comput. Sci. 3, 591-613 (1991). MSC: 68Q70 68Q05 68Q10 PDF BibTeX XML Cite \textit{V. Yodaiken}, in: Computer-aided verification '90. Proceedings of a 2nd DIMACS workshop, June 18-21, 1990, Rutgers Univ., New Brunswick, NJ, USA. Providence, RI: American Mathematical Society; New York, NY: Association for Computing Machinery. 591--613 (1991; Zbl 0789.68101)
Dybjer, Peter Inductive sets and families in Martin-Löf’s type theory and their set- theoretic semantics. (English) Zbl 0755.03033 Logical frameworks, Proc. 1st Annu. Workshop, Sophia-Antipolis/Fr. 1990, 280-306 (1991). Reviewer: M.W.Bunder (Wollongong) MSC: 03F35 03B40 PDF BibTeX XML Cite \textit{P. Dybjer}, in: Logical frameworks. Proceedings of the first annual workshop ''Logical frameworks: design, implementation and experiment'', held in Sophia- Antipolis, France, May 7-11, 1990. Cambridge etc.: Cambridge University Press. 280--306 (1991; Zbl 0755.03033)
Rathjen, Michael The role of parameters in bar rule and bar induction. (English) Zbl 0736.03024 J. Symb. Log. 56, No. 2, 715-730 (1991). Reviewer: G.Mints (Stanford) MSC: 03F35 PDF BibTeX XML Cite \textit{M. Rathjen}, J. Symb. Log. 56, No. 2, 715--730 (1991; Zbl 0736.03024) Full Text: DOI
Loebl, Martin; Nešetřil, Jaroslav Fast and slow growing (a combinatorial study of unprovability). (English) Zbl 0735.03017 Surveys in combinatorics, Proc. 13th Br. Comb. Conf., Guildford/UK 1991, Lond. Math. Soc. Lect. Note Ser. 166, 119-160 (1991). MSC: 03D20 03F30 03-02 PDF BibTeX XML
Arai, Toshiyasu Derivability conditions on Rosser’s provability predicates. (English) Zbl 0722.03041 Notre Dame J. Formal Logic 31, No. 4, 487-497 (1990). Reviewer: M.Yasuhara (Princeton) MSC: 03F30 PDF BibTeX XML Cite \textit{T. Arai}, Notre Dame J. Formal Logic 31, No. 4, 487--497 (1990; Zbl 0722.03041) Full Text: DOI
Ferreira, Fernando Polynomial time computable arithmetic. (English) Zbl 0707.03032 Logic and computation, Proc. Workshop, Pittsburgh/PA (USA) 1987, Contemp. Math. 106, 137-156 (1990). Reviewer: M.Tetruashvili MSC: 03D15 03F30 PDF BibTeX XML
Leivant, Daniel Computationally based set existence principles. (English) Zbl 0693.03037 Logic and computation, Proc. Workshop, Pittsburgh/PA (USA) 1987, Contemp. Math. 106, 197-211 (1990). MSC: 03F20 03F30 03F50 03D15 03D20 PDF BibTeX XML
Shen, Bai Ying Primitive recursive arithmetic. (Chinese) Zbl 0751.03029 Shanghai: Huadong Huagong Xueyuan Chubanshe. 433 p. (1990). Reviewer: Lei Qian MSC: 03F30 03D20 03-01 03-02 PDF BibTeX XML Cite \textit{B. Y. Shen}, Primitive recursive arithmetic (Chinese). Shanghai: Huadong Huagong Xueyuan Chubanshe (1990; Zbl 0751.03029)
Carbone, Alessandra; Montagna, Franco Rosser orderings in bimodal logics. (English) Zbl 0688.03010 Z. Math. Logik Grundlagen Math. 35, No. 4, 343-358 (1989). Reviewer: G.Mints MSC: 03B45 03F40 PDF BibTeX XML Cite \textit{A. Carbone} and \textit{F. Montagna}, Z. Math. Logik Grundlagen Math. 35, No. 4, 343--358 (1989; Zbl 0688.03010) Full Text: DOI
Drake, Frank R. On the Foundations of Mathematics in 1987. (English) Zbl 0688.03002 Logic colloq. ’87, Proc. Colloq., Granada/Spain 1987, Stud. Logic Found. Math. 129, 11-25 (1989). Reviewer: J.S.Ullian MSC: 03A05 03E30 03F35 03B10 03B30 PDF BibTeX XML
Feferman, Solomon Finitary inductively presented logics. (English) Zbl 0682.03031 Logic colloq. ’88, Proc. Colloq., Padova/Italy 1988, Stud. Logic Found. Math. 127, 191-220 (1989). Reviewer: Phan Dinh Dieu MSC: 03D70 PDF BibTeX XML
Duvall, Paul; Vaughan, Theresa P. Recursions for Carlitz triples. (English) Zbl 0671.10003 Fibonacci Q. 27, No. 2, 131-138 (1989). Reviewer: K.S.Williams MSC: 11A05 11A07 PDF BibTeX XML Cite \textit{P. Duvall} and \textit{T. P. Vaughan}, Fibonacci Q. 27, No. 2, 131--138 (1989; Zbl 0671.10003)
Tomás, Francisco On Hilbert’s program and the notion of recursive formalism. (Spanish) Zbl 0764.03023 An. Inst. Mat., Univ. Nac. Autón. Méx. 29, 87-151 (1989). Reviewer: E.Mendelson (Flushing) MSC: 03F50 03F30 03F60 PDF BibTeX XML Cite \textit{F. Tomás}, An. Inst. Mat., Univ. Nac. Autón. Méx. 29, 87--151 (1989; Zbl 0764.03023)
Feferman, Solomon Hilbert’s Program relativized: Proof-theoretical and foundational reductions. (English) Zbl 0656.03002 J. Symb. Log. 53, No. 2, 364-384 (1988). Reviewer: B.R.Boričić MSC: 03-03 03Fxx 03F30 PDF BibTeX XML Cite \textit{S. Feferman}, J. Symb. Log. 53, No. 2, 364--384 (1988; Zbl 0656.03002) Full Text: DOI
Sieg, Wilfried Provably recursive functionals of theories with Koenig’s lemma. (English) Zbl 0672.03045 Rend. Semin. Mat., Torino Fasc. Spec., 75-92 (1987). Reviewer: S.Artemov MSC: 03F35 PDF BibTeX XML
Atanassov, Krassimir T. More on the \(\Psi\)-function. I, II. (English) Zbl 0668.10010 Bull. Number Theory Relat. Top. 11, No. 1, 27-30, 31-36 (1987). Reviewer: I.Sándor MSC: 11A25 PDF BibTeX XML
Shen, Baiying The primitive recursive arithmetic in the first class \(A_ 01\). (Chinese. English summary) Zbl 0657.03027 J. Nanjing Univ., Nat. Sci. Ed. 23, No. 2, 243-253 (1987). Reviewer: Moh Shawkwei MSC: 03D99 03F30 PDF BibTeX XML
Bozhich, E. S. On arithmetic with the notion of “attainable number”. (English) Zbl 0645.03058 Math. USSR, Izv. 29, 477-510 (1987). MSC: 03F30 PDF BibTeX XML Cite \textit{E. S. Bozhich}, Math. USSR, Izv. 29, 477--510 (1987; Zbl 0645.03058) Full Text: DOI
Gordeev, L. On cut elimination in the presence of Peirce rule. (English) Zbl 0639.03059 Arch. Math. Logik Grundlagenforsch. 26, 147-164 (1987). Reviewer: O.Sonobe MSC: 03F05 03F20 03B10 PDF BibTeX XML Cite \textit{L. Gordeev}, Arch. Math. Logik Grundlagenforsch. 26, 147--164 (1987; Zbl 0639.03059) Full Text: DOI EuDML
Schwartz, Daniel G. A free-variable theory of primitive recursive arithmetic. (English) Zbl 0624.03042 Z. Math. Logik Grundlagen Math. 33, 147-157 (1987). MSC: 03F30 PDF BibTeX XML Cite \textit{D. G. Schwartz}, Z. Math. Logik Grundlagen Math. 33, 147--157 (1987; Zbl 0624.03042) Full Text: DOI
Schwartz, Daniel G. Semantic completeness of free-variable theories. (English) Zbl 0618.03028 Z. Math. Logik Grundlagen Math. 33, 441-452 (1987). MSC: 03F30 PDF BibTeX XML Cite \textit{D. G. Schwartz}, Z. Math. Logik Grundlagen Math. 33, 441--452 (1987; Zbl 0618.03028) Full Text: DOI
Schwartz, Daniel G. On the equivalence between logic-free and logic-bearing systems of primitive recursive arithmetic. (English) Zbl 0618.03027 Z. Math. Logik Grundlagen Math. 33, 245-253 (1987). MSC: 03F30 PDF BibTeX XML Cite \textit{D. G. Schwartz}, Z. Math. Logik Grundlagen Math. 33, 245--253 (1987; Zbl 0618.03027) Full Text: DOI
Mal’tsev, A. I. Algorithms and recursive functions. (Al’goritmy i rekursivnye funktsii). 2nd ed. Ed. and with a preface and an appendix by D. A. Zakharov. (Russian) Zbl 0664.03030 Moskva: Nauka. 368 p. R. 1.70 (1986). MSC: 03Dxx 03D20 03-01 03-02 03D45 03D25 03D35 03D10 03D40 03D03 03B25 68W99 11U05 11D99 PDF BibTeX XML
Bozhich, E. S. On arithmetic with the notion of “accessible number”. (Russian) Zbl 0634.03059 Izv. Akad. Nauk SSSR, Ser. Mat. 50, No. 6, 1123-1155 (1986). Reviewer: M.Tetruašvili MSC: 03F30 PDF BibTeX XML Cite \textit{E. S. Bozhich}, Izv. Akad. Nauk SSSR, Ser. Mat. 50, No. 6, 1123--1155 (1986; Zbl 0634.03059)
Howard, William The use of ordinals in the constructive foundations of mathematics. (English) Zbl 0623.03052 Logic, methodology and philosophy of science VII, Proc. 7th Int. Congr., Salzburg 1983, Stud. Logic Found. Math. 114, 83-94 (1986). Reviewer: H.Pfeiffer MSC: 03F15 03F50 03F35 03F10 03F05 PDF BibTeX XML
Kurata, Reijiro Paris-Harrington principles, reflection principles and transfinite induction up to \(\epsilon _ 0\). (English) Zbl 0603.03015 Ann. Pure Appl. Logic 31, 237-256 (1986). MSC: 03E30 PDF BibTeX XML Cite \textit{R. Kurata}, Ann. Pure Appl. Logic 31, 237--256 (1986; Zbl 0603.03015) Full Text: DOI
Shen, Baiying The primitive recursive arithmetic \(A^ 0\) 1 of the first class. (Chinese) Zbl 0633.03057 Acta Math. Sin. 28, 294-307 (1985). Reviewer: Moh Shawkwei MSC: 03F30 PDF BibTeX XML Cite \textit{B. Shen}, Acta Math. Sin. 28, 294--307 (1985; Zbl 0633.03057)
Cantini, Andrea Majorizing provably recursive functions in fragments of PA. (English) Zbl 0592.03046 Arch. Math. Logik Grundlagenforsch. 25, 21-31 (1985). Reviewer: M.Yasuhara MSC: 03F30 PDF BibTeX XML Cite \textit{A. Cantini}, Arch. Math. Logik Grundlagenforsch. 25, 21--31 (1985; Zbl 0592.03046) Full Text: DOI EuDML
Parlamento, Franco Rules and principles of restricted induction related to PRA. (Italian) Zbl 0591.03042 Atti degli incontri di logica matematica, Vol. 2, Siena/Italia 1983/84, 513-517 (1985). Reviewer: F.Montagna MSC: 03F30 PDF BibTeX XML
Cantini, Andrea On weak theories of sets and classes which are based on strict \(\Pi ^ 1_ 1\)-reflection. (English) Zbl 0553.03034 Z. Math. Logik Grundlagen Math. 31, 321-332 (1985). MSC: 03E99 03F99 PDF BibTeX XML Cite \textit{A. Cantini}, Z. Math. Logik Grundlagen Math. 31, 321--332 (1985; Zbl 0553.03034) Full Text: DOI
Parlamento, Franco PRA provability of Schmerl’s fine structure theorem. (English) Zbl 0606.03010 Rend. Semin. Mat., Torino 42, No. 2, 87-106 (1984). Reviewer: N.Both MSC: 03D65 03F15 PDF BibTeX XML Cite \textit{F. Parlamento}, Rend. Semin. Mat., Torino 42, No. 2, 87--106 (1984; Zbl 0606.03010)
Pearce, Jon A constructive consistency proof of a fragment of set theory. (English) Zbl 0599.03059 Ann. Pure Appl. Logic 27, 25-62 (1984). Reviewer: F.R.Drake MSC: 03F35 03E35 PDF BibTeX XML Cite \textit{J. Pearce}, Ann. Pure Appl. Logic 27, 25--62 (1984; Zbl 0599.03059) Full Text: DOI
Constable, R. L. Mathematics as programming. (English) Zbl 0571.68024 Logics of programs, Workshop, Pittsburgh/PA 1983, Lect. Notes Comput. Sci. 164, 116-128 (1984). Reviewer: A.Soil MSC: 68Q65 68N01 03B15 03D20 PDF BibTeX XML
Mo, Shaokui; Ding, Decheng The simplification of axioms of recursive arithmetic. (Chinese. English summary) Zbl 0566.03029 Chin. Ann. Math., Ser. A 5, 169-176 (1984). MSC: 03D99 11A99 PDF BibTeX XML Cite \textit{S. Mo} and \textit{D. Ding}, Chin. Ann. Math., Ser. A 5, 169--176 (1984; Zbl 0566.03029)
Shen, Baiying The primitive recursive arithmetic in the second class \(A^ 0(D)\). (Chinese) Zbl 0564.03036 Acta Math. Sin. 27, 345-363 (1984). Reviewer: C.T.Chong MSC: 03D20 PDF BibTeX XML Cite \textit{B. Shen}, Acta Math. Sin. 27, 345--363 (1984; Zbl 0564.03036)
Shen, Baiying The primitive recursive arithmetic in the first class \(B^ 11\). (Chinese) Zbl 0543.03033 Acta Math. Sin. 27, 203-207 (1984). Reviewer: C.T.Chong MSC: 03D99 PDF BibTeX XML Cite \textit{B. Shen}, Acta Math. Sin. 27, 203--207 (1984; Zbl 0543.03033)
Leivant, Daniel The optimality of induction as an axiomatization of arithmetic. (English) Zbl 0515.03018 J. Symb. Log. 48, 182-184 (1983). MSC: 03C62 03B10 PDF BibTeX XML Cite \textit{D. Leivant}, J. Symb. Log. 48, 182--184 (1983; Zbl 0515.03018) Full Text: DOI
Ter-Zakharyan, N. P. The possibilities of coding messages in various languages of formal arithmetic. (Russian) Zbl 0595.03054 Tr. Vychisl. Tsentra Akad. Nauk Arm. SSR Erevan. Gos. Univ. 10, 93-102 (1982). MSC: 03F30 03D20 PDF BibTeX XML Cite \textit{N. P. Ter-Zakharyan}, Tr. Vychisl. Tsentra Akad. Nauk Arm. SSR Erevan. Gos. Univ. 10, 93--102 (1982; Zbl 0595.03054)
Pfender, M.; Reiter, R.; Sartorius, M. Constructive arithmetics. (English) Zbl 0523.03049 Category theory. Applications to algebra, logic and topology, Proc. int. Conf., Gummersbach 1981, Lect. Notes Math. 962, 228-236 (1982). MSC: 03F65 03G30 03B30 PDF BibTeX XML
Friedman, Harvey M.; McAloon, Kenneth; Simpson, Stephen G. A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis. (English) Zbl 0522.03044 Patras Logic Symposion, Proc., Patras/Greece 1980, Stud. Logic Found. Math. 109, 197-230 (1982). MSC: 03F35 03C85 03D65 03H99 03F15 PDF BibTeX XML
Pla, Josep On the R-representability of primitive recursive functions. (Catalan) Zbl 0521.03025 Mathematical logic, Proc. 1st Catalonian Congr., Barcelona 1982, 101-105 (1982). MSC: 03D20 PDF BibTeX XML
Fahmy, M. H. A formal proof of Ackermann’s theorem. (English) Zbl 0572.03019 Proc. Math. Phys. Soc. Egypt 51, 1-6 (1981). MSC: 03D20 03F60 PDF BibTeX XML Cite \textit{M. H. Fahmy}, Proc. Math. Phys. Soc. Egypt 51, 1--6 (1981; Zbl 0572.03019)