The Number of Countable Models of a Complete Theory and of Its Inessential Extension

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发表日期：

2024年9月1日

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K. Zh. Kudaibergenov

摘要

It is proved that (a) there exists a complete countable theory having 2^ω countable models, some inessential extension of which has ω countable models, and that (b) there exists a complete countable theory having 2^ω countable models, some inessential extension of which has finitely many countable models. This gives an answer to the question of A. D. Taimanov.