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Applications of Kolmogorov complexity to computable model theory

  • Bakhadyr Khoussainov (a1), Pavel Semukhin (a2) and Frank Stephan (a3)

Abstract

In this paper we answer the following well-known open question in computable model theory. Does there exist a computable not ℵ0-categorical saturated structure with a unique computable isomor-phism 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 ℵ1-categorical but not ℵ0-categorical saturated -structure with a unique computable isomorphism type. In addition, using the construction we give an example of an ℵ1-categorical but not ℵ0-categorical theory whose only non-computable model is the prime one.

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Applications of Kolmogorov complexity to computable model theory

  • Bakhadyr Khoussainov (a1), Pavel Semukhin (a2) and Frank Stephan (a3)

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