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|Title:||Applications of kolmogorov complexity to computable model theory|
|Citation:||Khoussainov, B., Semukhin, P., Stephan, F. (2007-09). Applications of kolmogorov complexity to computable model theory. Journal of Symbolic Logic 72 (3) : 1041-1054. ScholarBank@NUS Repository. https://doi.org/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 N0- 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 N 1 -categorical but not N0-categorical saturated Σ1 0-structure with a unique computable isomorphism type. In addition, using the construction we give an example of an N 1-categorical but not N0-categorical theory whose only non-computable model is the prime one. © 2007, Association for Symbolic Logic.|
|Source Title:||Journal of Symbolic Logic|
|Appears in Collections:||Staff Publications|
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