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Turing degrees of complete formulas of almost prime models. (English. Russian original) Zbl 1485.03112

Algebra Logic 58, No. 3, 282-287 (2019); translation from Algebra Logika 58, No. 3, 417-425 (2019).

MSC:

03C57 Computable structure theory, computable model theory
03D28 Other Turing degree structures
03D45 Theory of numerations, effectively presented structures
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References:

[1] S. S. Goncharov and Yu. L. Ershov, Constructive Models, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999). · Zbl 1043.03518
[2] Mal’tsev, AI, On recursive Abelian groups, Dokl. Akad. Nauk SSSR, 146, 1009-1012 (1962) · Zbl 0156.01105
[3] Mal’tsev, AI, Constructive algebras. 1, Usp. Mat. Nauk, 16, 3-60 (1961)
[4] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973). · Zbl 0276.02032
[5] H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967). · Zbl 0183.01401
[6] S. Goncharov and B. Khoussainov, “Open problems in the theory of constructive algebraic systems,” Cont. Math., 257, Am. Math. Soc., Providence, RI (2000), pp. 145-170. · Zbl 0961.03037
[7] Nurtazin, AT, Strong and weak constructivizations and computable families, Algebra and Logic, 13, 177-184 (1974) · Zbl 0305.02061 · doi:10.1007/BF01463352
[8] Goncharov, SS, The problem of the number of non-autoequivalent constructivizations, Dokl. Akad. Nauk SSSR, 251, 271-274 (1980) · Zbl 0476.03045
[9] Goncharov, SS, Problem of number of nonautoequivalent constructivizations, Algebra and Logic, 19, 401-414 (1980) · Zbl 0476.03046 · doi:10.1007/BF01669323
[10] Goncharov, SS, Groups with a finite number of constructivizations, Dokl. Akad. Nauk SSSR, 256, 269-272 (1981) · Zbl 0496.20021
[11] Goncharov, SS; Molokov, AV; Romanovskii, NS, Nilpotent groups of finite algorithmic dimension, Sib. Math. J., 30, 63-68 (1989) · Zbl 0684.20025 · doi:10.1007/BF01054216
[12] Goncharov, SS, Computable single-valued numerations, Algebra and logic, 19, 325-356 (1980) · Zbl 0514.03029 · doi:10.1007/BF01669607
[13] Fokina, EB; Kalimullin, I.; Miller, R., Degrees of categoricity of computable structures, Arch. Math. Log., 49, 51-67 (2010) · Zbl 1184.03026 · doi:10.1007/s00153-009-0160-4
[14] Csima, BF; Franklin, JN; Shore, RA, Degrees of categoricity and the hyperarithmetic hierarchy, Notre Dame J. Form. Log., 54, 215-231 (2013) · Zbl 1311.03070 · doi:10.1215/00294527-1960479
[15] Bazhenov, NA, Degrees of categoricity for superatomic Boolean algebras, Algebra and Logic, 52, 179-187 (2013) · Zbl 1315.03052 · doi:10.1007/s10469-013-9233-x
[16] Anderson, B.; Csima, B., Degrees that are not degrees of categoricity, Notre Dame J. Form. Log., 57, 389-398 (2016) · Zbl 1436.03229
[17] Fokina, E.; Frolov, A.; Kalimullin, I., Categoricity spectra for rigid structures, Notre Dame J. Form. Log., 57, 45-57 (2016) · Zbl 1359.03030 · doi:10.1215/00294527-3322017
[18] Miller, R., d-Computable categoricity for algebraic fields, J. Symb. Log., 74, 1325-1351 (2009) · Zbl 1202.03044 · doi:10.2178/jsl/1254748694
[19] E. B. Fokina, V. Harizanov, and A. Melnikov, “Computable model theory,” in Turing’s Legacy: Developments from Turing’s Ideas in Logic, Lect. Notes Log., 42, R. Downey (ed.), Cambridge Univ. Press, Ass. Symb. Log., Cambridge (2014), pp. 124-194. · Zbl 1341.03002
[20] Bazhenov, NA, Autostability spectra for Boolean algebras, Algebra and Logic, 53, 502-505 (2014) · Zbl 1355.03028 · doi:10.1007/s10469-015-9311-3
[21] Goncharov, SS, Degrees of autostability relative to strong constructivizations, Trudy MIAN, 274, 119-129 (2011) · Zbl 1294.03025
[22] Palyutin, EA, Algebras of formulas for countably categorical theories, Coll. Math., 31, 157-159 (1974) · Zbl 0295.02029 · doi:10.4064/cm-31-2-157-159
[23] Schmerl, JH, A decidable ℵ_0-categorical theory with a non-recursive Ryll-Nardzewski function, Fund. Math., 98, 121-125 (1978) · Zbl 0372.02025 · doi:10.4064/fm-98-2-121-125
[24] N. Bazhenov, “Prime model with no degree of autostability relative to strong constructivizations,” in Lect. Notes Comput. Sci., 9136, Springer-Verlag, Berlin (2015), pp. 117-126. · Zbl 1461.03027
[25] S. S. Goncharov, “On the autostability of almost prime models relative to strong constructivizations,” Usp. Mat. Nauk, 65, No. 5(395), 107-142 (2010). · Zbl 1219.03038
[26] Morley, M., Decidable models, Israel J. Math., 25, 233-240 (1976) · Zbl 0361.02067 · doi:10.1007/BF02757002
[27] R. Miller, “Revisiting uniform computable categoricity: For the sixtieth birthday of prof. Rod Downey,” Lect. Notes Comp. Sci., 10010, Springer, Cham (2017), pp. 254-270. · Zbl 1485.03115
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