×

What makes the continuum \(\aleph_2\). (English) Zbl 1423.03194

Caicedo, Andrés Eduardo (ed.) et al., Foundations of mathematics. Logic at Harvard. Essays in honor of W. Hugh Woodin’s 60th birthday. Proceedings of the Logic at Harvard conference, Harvard University, Cambridge, MA, USA, March 27–29, 2015. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 690, 259-287 (2017).
For the entire collection see [Zbl 1367.03010].

MSC:

03E50 Continuum hypothesis and Martin’s axiom
03E35 Consistency and independence results
03E57 Generic absoluteness and forcing axioms
03E65 Other set-theoretic hypotheses and axioms
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abraham, U.; Shelah, S., Isomorphism types of Aronszajn trees, Israel J. Math., 50, 1-2, 75-113 (1985) · Zbl 0566.03032 · doi:10.1007/BF02761119
[2] Abraham, Uri; Rubin, Matatyahu; Shelah, Saharon, On the consistency of some partition theorems for continuous colorings, and the structure of \(\aleph_1\)-dense real order types, Ann. Pure Appl. Logic, 29, 2, 123-206 (1985) · Zbl 0585.03019 · doi:10.1016/0168-0072(84)90024-1
[3] Abraham, Uri; Todor{\v{c}}evi{\'c}, Stevo, Partition properties of \(\omega_1\) compatible with CH, Fund. Math., 152, 2, 165-181 (1997) · Zbl 0879.03015
[4] Asper{\'o}, David, Guessing and non-guessing of canonical functions, Ann. Pure Appl. Logic, 146, 2-3, 150-179 (2007) · Zbl 1116.03044 · doi:10.1016/j.apal.2007.02.002
[5] Asper{\'o}, David; Larson, Paul; Moore, Justin Tatch, Forcing axioms and the continuum hypothesis, Acta Math., 210, 1, 1-29 (2013) · Zbl 1312.03031 · doi:10.1007/s11511-013-0089-7
[6] D. Aspero and M. A. Mota, Measuring club-sequences together with the continuum large, J. Symbolic Logic, to appear. · Zbl 1422.03104
[7] Bagaria, Joan, Bounded forcing axioms as principles of generic absoluteness, Arch. Math. Logic, 39, 6, 393-401 (2000) · Zbl 0966.03047 · doi:10.1007/s001530050154
[8] Bagaria, Joan; Castells, Neus; Larson, Paul, An \(\Omega \)-logic primer. Set theory, Trends Math., 1-28 (2006), Birkh\`“auser, Basel · Zbl 1111.03046 · doi:10.1007/3-7643-7692-9\_1
[9] Baumgartner, James E., All \(\aleph_1\)-dense sets of reals can be isomorphic, Fund. Math., 79, 2, 101-106 (1973) · Zbl 0274.02037
[10] J. E. Baumgartner, Applications of the Proper Forcing Axiom. In Handbook of set-theoretic topology, 913-959. North-Holland, 1981. · Zbl 0556.03040
[11] Baumgartner, James E., Chains and antichains in \({\mathcal{P}}(\omega )\), J. Symbolic Logic, 45, 1, 85-92 (1980) · Zbl 0437.03027 · doi:10.2307/2273356
[12] Baumgartner, J.; Malitz, J.; Reinhardt, W., Embedding trees in the rationals, Proc. Nat. Acad. Sci. U.S.A., 67, 1748-1753 (1970) · Zbl 0209.01601
[13] Baumgartner, James E.; Taylor, Alan D., Saturation properties of ideals in generic extensions. I, Trans. Amer. Math. Soc., 270, 2, 557-574 (1982) · Zbl 0485.03022 · doi:10.2307/1999861
[14] Bekkali, M., Topics in set theory: Lebesgue measurability, large cardinals, forcing axioms, rho-functions, Lecture Notes in Mathematics 1476, viii+120 pp. (1991), Springer-Verlag, Berlin · Zbl 0729.03022 · doi:10.1007/BFb0098398
[15] Blass, Andreas, Groupwise density and related cardinals, Arch. Math. Logic, 30, 1, 1-11 (1990) · Zbl 0706.03036 · doi:10.1007/BF01793782
[16] Blass, Andreas, Near coherence of filters. II. Applications to operator ideals, the Stone-\v Cech remainder of a half-line, order ideals of sequences, and slenderness of groups, Trans. Amer. Math. Soc., 300, 2, 557-581 (1987) · Zbl 0647.03043 · doi:10.2307/2000357
[17] Blass, Andreas, Selective ultrafilters and homogeneity, Ann. Pure Appl. Logic, 38, 3, 215-255 (1988) · Zbl 0649.03036 · doi:10.1016/0168-0072(88)90027-9
[18] Blass, Andreas; Laflamme, Claude, Consistency results about filters and the number of inequivalent growth types, J. Symbolic Logic, 54, 1, 50-56 (1989) · Zbl 0673.03038 · doi:10.2307/2275014
[19] Blass, Andreas; Shelah, Saharon, There may be simple \(P_{\aleph_1} \)- and \(P_{\aleph_2} \)-points and the Rudin-Keisler ordering may be downward directed, Ann. Pure Appl. Logic, 33, 3, 213-243 (1987) · Zbl 0634.03047 · doi:10.1016/0168-0072(87)90082-0
[20] Blass, Andreas; Shelah, Saharon, Near coherence of filters. III. A simplified consistency proof, Notre Dame J. Formal Logic, 30, 4, 530-538 (1989) · Zbl 0702.03030 · doi:10.1305/ndjfl/1093635236
[21] Blass, Andreas; Weiss, Gary, A characterization and sum decomposition for operator ideals, Trans. Amer. Math. Soc., 246, 407-417 (1978) · Zbl 0414.47017 · doi:10.2307/1997982
[22] Brendle, J.; Larson, P.; Todor{\v{c}}evi{\'c}, S., Rectangular axioms, perfect set properties and decomposition, Bull. Cl. Sci. Math. Nat. Sci. Math., 33, 91-130 (2008) · Zbl 1265.03044
[23] Caicedo, Andr{\'e}s Eduardo; Veli{\v{c}}kovi{\'c}, Boban, The bounded proper forcing axiom and well orderings of the reals, Math. Res. Lett., 13, 2-3, 393-408 (2006) · Zbl 1113.03039 · doi:10.4310/MRL.2006.v13.n3.a5
[24] G. Cantor. Ein Beitrag zur Mannigfaltigkeitslehre. Journal fur die Reine und Angewandte Mathematik, 37:127-142, 1887.
[25] Choquet, Gustave, Construction d’ultrafiltres sur N, Bull. Sci. Math. (2), 92, 41-48 (1968) · Zbl 0157.53101
[26] G. Choquet, Deux classes remarquables d’ultrafiltres sur N. Bull. Sci. Math. (2), 92:143-153, 1968. · Zbl 0162.26201
[27] Christensen, J. P. R., Topology and Borel structure, iii+133 pp. (1974), North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York · Zbl 0273.28001
[28] Cummings, James, Compactness and incompactness phenomena in set theory. Logic Colloquium ’01, Lect. Notes Log. 20, 139-150 (2005), Assoc. Symbol. Logic, Urbana, IL · Zbl 1081.03046
[29] Cummings, James, Large cardinal properties of small cardinals. Set theory, Cura\c cao, 1995; Barcelona, 1996, 23-39 (1998), Kluwer Acad. Publ., Dordrecht · Zbl 0949.03040
[30] Cummings, James; Foreman, Matthew; Magidor, Menachem, Squares, scales and stationary reflection, J. Math. Log., 1, 1, 35-98 (2001) · Zbl 0988.03075 · doi:10.1142/S021906130100003X
[31] Dales, H. G.; Esterle, J., Discontinuous homomorphisms from \(C(X)\), Bull. Amer. Math. Soc., 83, 2, 257-259 (1977) · Zbl 0341.46037
[32] Dales, H. G.; Woodin, W. H., An introduction to independence for analysts, London Mathematical Society Lecture Note Series 115, xiv+241 pp. (1987), Cambridge University Press, Cambridge · Zbl 0629.03030 · doi:10.1017/CBO9780511662256
[33] Devlin, Keith J., The Yorkshireman’s guide to proper forcing. Surveys in set theory, London Math. Soc. Lecture Note Ser. 87, 60-115 (1983), Cambridge Univ. Press, Cambridge · Zbl 0524.03041 · doi:10.1017/CBO9780511758867.003
[34] Devlin, Keith J.; Shelah, Saharon, A weak version of \(\diamondsuit\) which follows from \(2^{\aleph_0}<2^{\aleph_1} \), Israel J. Math., 29, 2-3, 239-247 (1978) · Zbl 0403.03040
[35] Di Prisco, Carlos Augusto; Todorcevic, Stevo, Perfect-set properties in \(L({\bf R})[U]\), Adv. Math., 139, 2, 240-259 (1998) · Zbl 0929.03050 · doi:10.1006/aima.1998.1752
[36] Dow, Alan; Hart, Klaas Pieter, The measure algebra does not always embed, Fund. Math., 163, 2, 163-176 (2000) · Zbl 1010.28003
[37] Dushnik, Ben; Miller, E. W., Concerning similarity transformations of linearly ordered sets, Bull. Amer. Math. Soc., 46, 322-326 (1940) · JFM 66.0199.02
[38] Eisworth, Todd, Selective ultrafilters and \(\omega \to (\omega )^\omega \), Proc. Amer. Math. Soc., 127, 10, 3067-3071 (1999) · Zbl 0922.03062 · doi:10.1090/S0002-9939-99-04835-2
[39] T. Eisworth, J, Tatch Moore. Iterated forcing and the Continuum Hypothesis. In Appalachian set theory 2006-2012, London Math Society Lecture Notes Series, 406:207-244. Cambridge University Press, 2013. · Zbl 1367.03088
[40] Esterle, Jean, Kaplansky’s and Michael’s problems: a survey, Ann. Funct. Anal., 3, 2, 66-88 (2012) · Zbl 1263.46037 · doi:10.15352/afa/1399899933
[41] Farah, Ilijas, All automorphisms of the Calkin algebra are inner, Ann. of Math. (2), 173, 2, 619-661 (2011) · Zbl 1250.03094 · doi:10.4007/annals.2011.173.2.1
[42] I. Farah, Analytic quotients: theory of liftings for quotients over analytic ideals on the integers. Mem. Amer. Math. Soc., 148(702), 2000. · Zbl 0966.03045
[43] I. Farah, Dimension phenomena associated with \(\mathbb{N} \)-spaces. Topology Appl., 125(2):279-297, 2002. · Zbl 1027.54034
[44] Fedor{\v{c}}uk, V. V., A bicompactum whose infinite closed subsets are all \(n\)-dimensional, Mat. Sb. (N.S.), 96(138), 41-62, 167 (1975) · Zbl 0308.54028
[45] Feferman, Solomon; Friedman, Harvey M.; Maddy, Penelope; Steel, John R., Does mathematics need new axioms?, Bull. Symbolic Logic, 6, 4, 401-446 (2000) · Zbl 0977.03002 · doi:10.2307/420965
[46] Feng, Qi, Homogeneity for open partitions of pairs of reals, Trans. Amer. Math. Soc., 339, 2, 659-684 (1993) · Zbl 0795.03065 · doi:10.2307/2154292
[47] Foreman, Matthew, Has the continuum hypothesis been settled?. Logic Colloquium ’03, Lect. Notes Log. 24, 56-75 (2006), Assoc. Symbol. Logic, La Jolla, CA · Zbl 1107.03061
[48] Foreman, Matthew, Ideals and generic elementary embeddings. Handbook of set theory. Vols. 1, 2, 3, 885-1147 (2010), Springer, Dordrecht · Zbl 1198.03050 · doi:10.1007/978-1-4020-5764-9\_14
[49] Foreman, Matthew, Potent axioms, Trans. Amer. Math. Soc., 294, 1, 1-28 (1986) · Zbl 0614.03051 · doi:10.2307/2000115
[50] Foreman, Matthew; Magidor, Menachem, Large cardinals and definable counterexamples to the continuum hypothesis, Ann. Pure Appl. Logic, 76, 1, 47-97 (1995) · Zbl 0837.03040 · doi:10.1016/0168-0072(94)00031-W
[51] Foreman, M.; Magidor, M.; Shelah, S., Martin’s maximum, saturated ideals, and nonregular ultrafilters. I, Ann. of Math. (2), 127, 1, 1-47 (1988) · Zbl 0645.03028 · doi:10.2307/1971415
[52] Foreman, Matthew; Todorcevic, Stevo, A new L\`“owenheim-Skolem theorem, Trans. Amer. Math. Soc., 357, 5, 1693-1715 (2005) · Zbl 1082.03034 · doi:10.1090/S0002-9947-04-03445-2
[53] D. H. Fremlin. Consequences of Martin’s Axiom. Cambridge University Press, 1984. · Zbl 0551.03033
[54] Galvin, Fred, Chain conditions and products, Fund. Math., 108, 1, 33-48 (1980) · Zbl 0366.04011
[55] Gitik, Moti, Nonsplitting subset of \({\mathcal{P}}_\kappa (\kappa^+)\), J. Symbolic Logic, 50, 4, 881-894 (1986) (1985) · Zbl 0601.03021 · doi:10.2307/2273978
[56] K. Godel, What is Cantor’s continuum problem? Amer. Math. Monthly, 54:515-525, 1947. · Zbl 0038.03003
[57] K. Godel, Some considerations leading to the probable conclusion that the true power of the continuum is \(_2. In\) Kurt Godel: collected works, v. III, 420-422, Oxford University Press, Oxford, 1995.
[58] F. Hausdorff, Die Graduierung nach dem Endverlauf. Abhandlungen Konig. Sachsische Gesellschaft Wissenschaften, Math.-Phys. Kl., 296-334, 1909. · JFM 40.0446.02
[59] Haydon, Richard, On dual \(L^1\)-spaces and injective bidual Banach spaces, Israel J. Math., 31, 2, 142-152 (1978) · Zbl 0407.46018 · doi:10.1007/BF02760545
[60] W. Hurewicz. Une remarque sur l’hypothese du continu. Fund. Math., 19:8-9, 1932. · Zbl 0005.19601
[61] Just, Winfried, A modification of Shelah’s oracle-c.c.with applications, Trans. Amer. Math. Soc., 329, 1, 325-356 (1992) · Zbl 0753.03021 · doi:10.2307/2154091
[62] Just, Winfried, A weak version of \({\rm AT}\) from \({\rm OCA}\). Set theory of the continuum, Berkeley, CA, 1989, Math. Sci. Res. Inst. Publ. 26, 281-291 (1992), Springer, New York · Zbl 0824.04003 · doi:10.1007/978-1-4613-9754-0\_17
[63] Just, Winfried; Krawczyk, Adam, On certain Boolean algebras \({\mathcal{P}}(\omega )/I\), Trans. Amer. Math. Soc., 285, 1, 411-429 (1984) · Zbl 0519.06011 · doi:10.2307/1999489
[64] Kanamori, Akihiro, The higher infinite: Large cardinals in set theory from their beginnings, Springer Monographs in Mathematics, xxii+536 pp. (2003), Springer-Verlag, Berlin · Zbl 1022.03033
[65] Kaplansky, Irving, Normed algebras, Duke Math. J., 16, 399-418 (1949) · Zbl 0033.18701
[66] Kunen, Kenneth, A compact \(L\)-space under CH, Topology Appl., 12, 3, 283-287 (1981) · Zbl 0466.54015 · doi:10.1016/0166-8641(81)90006-7
[67] K. Kunen, Some points in \(N\). Math. Proc. Cambridge Philos. Soc., 80(3):385-398, 1976. · Zbl 0345.02047
[68] Dj. Kurepa. Ensembles ordonnes et ramifies. Publ. Math. Univ. Belgrade, 4:1-138, 1935. · Zbl 0014.39401
[69] Laflamme, Claude, Equivalence of families of functions on the natural numbers, Trans. Amer. Math. Soc., 330, 1, 307-319 (1992) · Zbl 0759.03025 · doi:10.2307/2154166
[70] Larson, Paul B., The filter dichotomy and medial limits, J. Math. Log., 9, 2, 159-165 (2009) · Zbl 1207.03055 · doi:10.1142/S0219061309000872
[71] P. B. Larson, Martin’s maximum and definability in \(H(_2)\). Ann. Pure Appl. Logic, 156(1):110-122, 2008. · Zbl 1153.03035
[72] P. B. Larson, Martin’s maximum and the \(\mathbb{P}_{\text{max}}\) axiom. Ann. Pure Appl. Logic, 106(1-3):135-149, 2000. · Zbl 0973.03068
[73] Larson, Paul B., The stationary tower: Notes on a course by W. Hugh Woodin, University Lecture Series 32, x+132 pp. (2004), American Mathematical Society, Providence, RI · Zbl 1072.03031 · doi:10.1090/ulect/032
[74] Laver, Richard, On Fra\`“\i ss\'”e’s order type conjecture, Ann. of Math. (2), 93, 89-111 (1971) · Zbl 0208.28905
[75] Maddy, Penelope, Believing the axioms. I, J. Symbolic Logic, 53, 2, 481-511 (1988) · Zbl 0652.03033 · doi:10.2307/2274520
[76] Maddy, Penelope, Believing the axioms. II, J. Symbolic Logic, 53, 3, 736-764 (1988) · Zbl 0656.03034 · doi:10.2307/2274569
[77] Martinez-Ranero, Carlos, Well-quasi-ordering Aronszajn lines, Fund. Math., 213, 3, 197-211 (2011) · Zbl 1235.03072 · doi:10.4064/fm213-3-1
[78] Mathias, A. R. D., Happy families, Ann. Math. Logic, 12, 1, 59-111 (1977) · Zbl 0369.02041
[79] Meyer, P. A., Limites m\'ediales, d’apr\`“es Mokobodzki. S\'”eminaire de Probabilit\'es, VII (Univ. Strasbourg, ann\'ee universitaire 1971-1972), 198-204. Lecture Notes in Math., Vol. 321 (1973), Springer, Berlin · Zbl 0262.28005
[80] Moore, Justin Tatch, A five element basis for the uncountable linear orders, Ann. of Math. (2), 163, 2, 669-688 (2006) · Zbl 1143.03026 · doi:10.4007/annals.2006.163.669
[81] Moore, Justin Tatch, Forcing axioms and the continuum hypothesis. Part II: transcending \(\omega_1\)-sequences of real numbers, Acta Math., 210, 1, 173-183 (2013) · Zbl 1312.03032 · doi:10.1007/s11511-013-0092-z
[82] Moore, Justin Tatch, Open colorings, the continuum and the second uncountable cardinal, Proc. Amer. Math. Soc., 130, 9, 2753-2759 (electronic) (2002) · Zbl 0994.03046 · doi:10.1090/S0002-9939-02-06376-1
[83] J. T. Moore, The Proper Forcing Axiom. Proceedings of the 2010 ICM, Hyderabad, India, 2:3-29, Hindustan Book Agency, 2010. · Zbl 1258.03075
[84] J. T. Moore, Set mapping reflection. J. Math. Log., 5(1):87-97, 2005. · Zbl 1082.03042
[85] J. T. Moore, A universal Aronszajn line. Math. Res. Lett., 16(1):121-131, 2009. · Zbl 1179.03055
[86] Morayne, M., On differentiability of Peano type functions, Colloq. Math., 48, 2, 261-264 (1984) · Zbl 0597.26015
[87] Nyikos, P., Progress on countably compact spaces. General topology and its relations to modern analysis and algebra, VI , Prague, 1986, Res. Exp. Math. 16, 379-410 (1988), Heldermann, Berlin · Zbl 0647.54020
[88] P. Nyikos, On first countable, countably compact spaces. III. The problem of obtaining separable noncompact examples. In Open problems in topology, 127-161, North-Holland, Amsterdam, 1990.
[89] Parovi{\v{c}}enko, I. I., On a universal bicompactum of weight \(\aleph \), Dokl. Akad. Nauk SSSR, 150, 36-39 (1963) · Zbl 0171.21301
[90] Phillips, N. Christopher; Weaver, Nik, The Calkin algebra has outer automorphisms, Duke Math. J., 139, 1, 185-202 (2007) · Zbl 1220.46040 · doi:10.1215/S0012-7094-07-13915-2
[91] Rado, R., Covering theorems for ordered sets, Proc. London Math. Soc. (2), 50, 509-535 (1949) · Zbl 0032.14803
[92] Rado, Richard, Theorems on intervals of ordered sets, Discrete Math., 35, 199-201 (1981) · Zbl 0463.06001 · doi:10.1016/0012-365X(81)90208-9
[93] Rudin, Mary Ellen, Composants and \(\beta N\). Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970), 117-119 (1970), Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash. · Zbl 0194.54703
[94] Rudin, Walter, Homogeneity problems in the theory of \v Cech compactifications, Duke Math. J., 23, 409-419 (1956) · Zbl 0073.39602
[95] Shelah, Saharon, Cardinal arithmetic, Oxford Logic Guides 29, xxxii+481 pp. (1994), The Clarendon Press, Oxford University Press, New York · Zbl 0848.03025
[96] Shelah, Saharon, Decomposing uncountable squares to countably many chains, J. Combinatorial Theory Ser. A, 21, 1, 110-114 (1976) · Zbl 0366.04009
[97] Shelah, Saharon, Groupwise density cannot be much bigger than the unbounded number, MLQ Math. Log. Q., 54, 4, 340-344 (2008) · Zbl 1148.03034 · doi:10.1002/malq.200710032
[98] S. Shelah, Proper forcing. Lecture Notes in Mathematics, 940. Springer-Verlag, Berlin, 1982. · Zbl 0495.03035
[99] S. Shelah, Proper and Improper Forcing. Springer-Verlag, Berlin, second edition, 1998. · Zbl 0889.03041
[100] Shelah, Saharon, Reflection implies the SCH, Fund. Math., 198, 2, 95-111 (2008) · Zbl 1147.03027 · doi:10.4064/fm198-2-1
[101] Shelah, Saharon; Woodin, Hugh, Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable, Israel J. Math., 70, 3, 381-394 (1990) · Zbl 0705.03028 · doi:10.1007/BF02801471
[102] Sierpi{\'n}ski, Wac{\l }aw, Hypoth\`“ese du continu, xvii+274 pp. (1956), Chelsea Publishing Company, New York, N. Y. · Zbl 0075.00903
[103] Solovay, R. M.; Tennenbaum, S., Iterated Cohen extensions and Souslin’s problem, Ann. of Math. (2), 94, 201-245 (1971) · Zbl 0244.02023
[104] Steel, John; Zoble, Stuart, Determinacy from strong reflection, Trans. Amer. Math. Soc., 366, 8, 4443-4490 (2014) · Zbl 1359.03038 · doi:10.1090/S0002-9947-2013-06058-8
[105] Talagrand, Michel, S\'eparabilit\'e vague dans l’espace des mesures sur un compact, Israel J. Math., 37, 1-2, 171-180 (1980) · Zbl 0445.46022 · doi:10.1007/BF02762878
[106] Todor{\v{c}}evi{\'c}, S., On a conjecture of R. Rado, J. London Math. Soc. (2), 27, 1, 1-8 (1983) · Zbl 0524.03033 · doi:10.1112/jlms/s2-27.1.1
[107] S. Todorcevic, Remarks on chain conditions in products. Composito Math., 55(3):295-302, 1985. · Zbl 0583.54003
[108] Todor{\v{c}}evi{\'c}, Stevo, Directed sets and cofinal types, Trans. Amer. Math. Soc., 290, 2, 711-723 (1985) · Zbl 0592.03037 · doi:10.2307/2000309
[109] S. Todorcevic, Partition Problems In Topology. Amer. Math. Soc., 1989. · Zbl 0659.54001
[110] Todor{\v{c}}evi{\'c}, Stevo, Remarks on Martin’s axiom and the continuum hypothesis, Canad. J. Math., 43, 4, 832-851 (1991) · Zbl 0776.03024 · doi:10.4153/CJM-1991-048-8
[111] S. Todorcevic, Conjectures of Chang and Rado and cardinal arithmetic. In Finite and infinite combinatorics in sets and logic, of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 411:385-398, Kluwer Acad. Publ., 1993. · Zbl 0844.03027
[112] Todorcevic, Stevo, A classification of transitive relations on \(\omega_1\), Proc. London Math. Soc. (3), 73, 3, 501-533 (1996) · Zbl 0870.04001 · doi:10.1112/plms/s3-73.3.501
[113] S. Todorcevic, Comparing the continuum with the first two uncountable cardinals. In Logic and scientific methods (Florence, 1995), 145-155. Kluwer Acad. Publ., Dordrecht, 1997. · Zbl 0906.03050
[114] Todor{\v{c}}evi{\'c}, Stevo, A dichotomy for P-ideals of countable sets, Fund. Math., 166, 3, 251-267 (2000) · Zbl 0968.03049
[115] Todor{\v{c}}evi{\'c}, Stevo, Generic absoluteness and the continuum, Math. Res. Lett., 9, 4, 465-471 (2002) · Zbl 1028.03040 · doi:10.4310/MRL.2002.v9.n4.a6
[116] S. Todorcevic, Notes on Forcing Axioms, volume 26 of Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore. World Scientific, Singapore, 2014. · Zbl 1294.03007
[117] Todor{\v{c}}evi{\'c}, Stevo, Partitioning pairs of countable ordinals, Acta Math., 159, 3-4, 261-294 (1987) · Zbl 0658.03028 · doi:10.1007/BF02392561
[118] Todor{\v{c}}evi{\'c}, Stevo, Oscillations of real numbers. Logic colloquium ’86, Hull, 1986, Stud. Logic Found. Math. 124, 325-331 (1988), North-Holland, Amsterdam · Zbl 0638.04003 · doi:10.1016/S0049-237X(09)70663-9
[119] S. Todorcevic, Reflecting stationary sets. handwritten notes, October 1984.
[120] S. Todorcevic, Walks on ordinals and their characteristics. Progress in Mathematics, 263, Birkhauser, 2007. · Zbl 1148.03004
[121] Todorchevich, S.; Farah, I., Some applications of the method of forcing, Yenisei Series in Pure and Applied Mathematics, iv+148 pp. (1995), Yenisei, Moscow; Lyc\'ee, Troitsk · Zbl 1089.03500
[122] Todor{\v{c}}evi{\'c}, S.; Veli{\v{c}}kovi{\'c}, B., Martin’s axiom and partitions, Compositio Math., 63, 3, 391-408 (1987) · Zbl 0643.03033
[123] Veli{\v{c}}kovi{\'c}, Boban, Forcing axioms and stationary sets, Adv. Math., 94, 2, 256-284 (1992) · Zbl 0785.03031 · doi:10.1016/0001-8708(92)90038-M
[124] Viale, Matteo, The proper forcing axiom and the singular cardinal hypothesis, J. Symbolic Logic, 71, 2, 473-479 (2006) · Zbl 1098.03053 · doi:10.2178/jsl/1146620153
[125] M. Viale, A family of covering properties. Math. Res. Lett., 15(2):221-238, 2008. · Zbl 1146.03033
[126] Viale, Matteo, Category forcings, \( \mathsf{MM}^{+++} \), and generic absoluteness for the theory of strong forcing axioms, J. Amer. Math. Soc., 29, 3, 675-728 (2016) · Zbl 1403.03108 · doi:10.1090/jams/844
[127] Woodin, W. Hugh, The axiom of determinacy, forcing axioms, and the nonstationary ideal, de Gruyter Series in Logic and its Applications 1, vi+934 pp. (1999), Walter de Gruyter & Co., Berlin · Zbl 0954.03046 · doi:10.1515/9783110804737
[128] W. H, Woodin, The continuum hypothesis. I. Notices Amer. Math. Soc., 48(6):567-576, 2001. · Zbl 0992.03063
[129] W. H, Woodin, The continuum hypothesis. II. Notices Amer. Math. Soc., 48(7):681-690, 2001. · Zbl 1047.03041
[130] Woodin, W. Hugh, Strong axioms of infinity and the search for \(V\). Proceedings of the International Congress of Mathematicians. Volume I, 504-528 (2010), Hindustan Book Agency, New Delhi · Zbl 1252.03001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.