An Old Friend Revisited: Countable Models of ω-Stable Theories
Michael C. Laskowski
Source: Notre Dame J. Formal Logic Volume 48, Number 1
(2007), 133-141.
Abstract
We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1172787550
Digital Object Identifier: doi:10.1305/ndjfl/1172787550
Mathematical Reviews number (MathSciNet): MR2289902
Zentralblatt MATH identifier: 1130.03026
References
[1] Becker, H., and A. S. Kechris, ``Borel actions of Polish groups,'' American Mathematical Society. Bull. New Ser., vol. 28 (1993), pp. 334--41.
Mathematical Reviews (MathSciNet): MR1185149
Zentralblatt MATH: 0781.03033
Digital Object Identifier: doi:10.1090/S0273-0979-1993-00383-5
[2] Bouscaren, E., and D. Lascar, "Countable models of nonmultidimensional $\aleph \sb0$"-stable theories, The Journal of Symbolic Logic, vol. 48 (1983), pp. 197--205.
Mathematical Reviews (MathSciNet): MR693263
Zentralblatt MATH: 0517.03008
Digital Object Identifier: doi:10.2307/2273335
Project Euclid: euclid.jsl/1183741205
[3] Friedman, H., and L. Stanley, "A Borel reducibility theory for classes of countable structures", The Journal of Symbolic Logic, vol. 54 (1989), pp. 894--914.
Mathematical Reviews (MathSciNet): MR1011177
Zentralblatt MATH: 0692.03022
Digital Object Identifier: doi:10.2307/2274750
Project Euclid: euclid.jsl/1183743025
[4] Harrington, L., and M. Makkai, "An exposition of Shelah's `main gap': Counting uncountable models of $\omega$"-stable and superstable theories, Notre Dame Journal of Formal Logic, vol. 26 (1985), pp. 139--77.
Mathematical Reviews (MathSciNet): MR783594
Zentralblatt MATH: 0589.03015
Digital Object Identifier: doi:10.1305/ndjfl/1093870822
Project Euclid: euclid.ndjfl/1093870822
[5] Hjorth, G., and A. S. Kechris, "Recent developments in the theory of Borel reducibility", Fundamenta Mathematicae, vol. 170 (2001), pp. 21--52. Dedicated to the memory of Jerzy Łoś.
Mathematical Reviews (MathSciNet): MR1881047
Zentralblatt MATH: 0992.03055
[6] Laskowski, M. C., and S. Shelah, "Borel completeness of some $\aleph_0$-stable theories", in preparation.
[7] Marker, D., "The number of countable differentially closed fields", Notre Dame Journal of Formal Logic, vol. 48 (2007), pp. 99--113 (electronic).
Mathematical Reviews (MathSciNet): MR2289900
Digital Object Identifier: doi:10.1305/ndjfl/1172787548
Project Euclid: euclid.ndjfl/1172787548
Zentralblatt MATH: 1128.03023
[8] Shelah, S., Classification Theory and the Number of Nonisomorphic Models, 2d edition, vol. 92 of Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1990.
Mathematical Reviews (MathSciNet): MR1083551
Zentralblatt MATH: 0713.03013
[9] Shelah, S., L. Harrington, and M. Makkai, "A proof of Vaught's conjecture for $\omega$"-stable theories, Israel Journal of Mathematics, vol. 49 (1984), pp. 259--80.
Mathematical Reviews (MathSciNet): MR788270
Zentralblatt MATH: 0584.03021
Digital Object Identifier: doi:10.1007/BF02760651
[10] Shelah, S., "Characterizing an $\aleph\sb \epsilon$"-saturated model of superstable NDOP theories by its $\Bbb L\sb\infty,\aleph\sb \epsilon$-theory, Israel Journal of Mathematics, vol. 140 (2004), pp. 61--111.
Mathematical Reviews (MathSciNet): MR2054839
Zentralblatt MATH: 1059.03024
Digital Object Identifier: doi:10.1007/BF02786627
[11] Vaught, R., "Invariant sets in topology and logic", Fundamenta Mathematicae, vol. 82 (1974/75), pp. 269--94. Collection of articles dedicated to Andrzej Mostowski on his 60th birthday, VII.
Mathematical Reviews (MathSciNet): MR0363912
Zentralblatt MATH: 0309.02068
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