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September 2007 Applications of Kolmogorov complexity to computable model theory
B. Khoussainov, P. Semukhin, F. Stephan
J. Symbolic Logic 72(3): 1041-1054 (September 2007). DOI: 10.2178/jsl/1191333855

Abstract

In this paper we answer the following well-known open question in computable model theory. Does there exist a computable not $\aleph_0$-categorical saturated structure with a unique computable isomorphism type? Our answer is affirmative and uses a construction based on Kolmogorov complexity. With a variation of this construction, we also provide an example of an $\aleph_1$-categorical but not $\aleph_0$-categorical saturated $\Sigma^0_1$-structure with a unique computable isomorphism type. In addition, using the construction we give an example of an $\aleph_1$-categorical but not $\aleph_0$-categorical theory whose only non-computable model is the prime one.

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B. Khoussainov. P. Semukhin. F. Stephan. "Applications of Kolmogorov complexity to computable model theory." J. Symbolic Logic 72 (3) 1041 - 1054, September 2007. https://doi.org/10.2178/jsl/1191333855

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

zbMATH: 1127.03031
MathSciNet: MR2354914
Digital Object Identifier: 10.2178/jsl/1191333855

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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