Computable Limit Models
In the paper we construct a complete theory having exactly 6 countable models up to isomorphism, such that there are two limits over a powerful type models, one of which has a computable presentation and the other does not.
1. Gavryushkin,A., Computable Models of Ehrenfeucht Theories, Ph.D. thesis, Novosibirsk, 2009.
2. Goncharov,S., Constructive models of ℵ1-categorical theories, Mat. Zametki, 23, 885–889, 1978.
3. Khisamiev,N.,CriterionforConstructivizabilityofaDirectSumofCyclicp-groups, Izvestiya Akademii Nauk Kazakhskoi SSR. Seriya Fiziko-Matematicheskaya, 86, 1, 51–55, 1981.
4. Khoussainov,B., Nies,A., Shore,R., Computable Models of Theories with Few Models, Notre Dame Journal of Formal Logic, 38, 2, 165–178, 1997.
5. Nies,A.,ANewSpectrum ofRecursiveModels, Notre Dame Journal of Formal Logic, 40, 3, 307–314, 1999.
6. Sudoplatov,S., Complete theories with finitely many countable models, Algebra and Logic, 43, 1, 62–69, 2004.