Remarks on convergence of Morley sequences
Karim Khanaki

TL;DR
This paper refines existing results on Morley sequences convergence, introduces the concept of eventual NIP, and provides new characterizations of generically stable types, advancing the understanding of model-theoretic stability and convergence properties.
Contribution
It improves the understanding of Morley sequence convergence, introduces eventual NIP, and offers new characterizations of generically stable types in countable theories.
Findings
Refined equivalences of convergent Morley sequences.
Introduced the notion of eventual NIP.
Provided new characterizations of generically stable types.
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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms
