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|Title:||Automatic models of first order theories|
|Source:||Semukhin, P., Stephan, F. (2013-09). Automatic models of first order theories. Annals of Pure and Applied Logic 164 (9) : 837-854. ScholarBank@NUS Repository. https://doi.org/10.1016/j.apal.2013.03.001|
|Abstract:||Khoussainov and Nerode (2008)  posed various open questions on model-theoretic properties of automatic structures. In this work we answer some of these questions by showing the following results: (1) There is an uncountably categorical but not countably categorical theory for which only the prime model is automatic; (2) There are complete theories with exactly 3, 4, 5,... countable models, respectively, and every countable model is automatic; (3) There is a complete theory for which exactly 2 models have an automatic presentation; (4) If LOGSPACE=P then there is an uncountably categorical but not countably categorical theory for which the prime model does not have an automatic presentation but all the other countable models are automatic; (5) There is a complete theory with countably many countable models for which the saturated model has an automatic presentation but the prime model does not have one. © 2013 Elsevier B.V.|
|Source Title:||Annals of Pure and Applied Logic|
|Appears in Collections:||Staff Publications|
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