Remarks on convergence of Morley sequences
arXiv:2110.15411 · doi:10.1017/jsl.2023.18
Abstract
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 , 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.
(27 pages) Final version incorporating referee comments; Proposition 3.9 is new; accepted to Journal of Symbolic Logic