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arXiv:2110.15411 [math.LO]AbstractReferencesReviewsResources

Remarks on convergence of Morley sequences

Karim Khanaki

Published 2021-10-28, updated 2022-07-14Version 6

We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and give a variant of [KP18, Corollary 2.2]. Finally, we give new characterizations of generically stable types (for countable theories) and reinforce the main result of Pillay [P18] on the model-theoretic meaning of Grothendieck's double limit theorem.

Comments: (23 pages) In this new version (1) a model-theoretic argument of Claim 2 in Theorem 2.11 is suggested by Predrag Tanovi\'c, (2) Claim 0 in Theorem 2.11 has been proven, (3) Fact 2.10 has been rewritten. (Theorem 4.10 reinforces the main result of the following paper on the model-theoretic meaning of Grothendieck's double limit theorem: arXiv:1703.04761 )
Categories: math.LO
Subjects: 03C45
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