Morley sequences in dependent theories

TL;DR

This paper characterizes Morley sequences in dependent theories, explores their properties, and introduces strict Morley sequences, providing new insights into their structure and stability conditions.

Contribution

It generalizes Poizat's special sequences, characterizes generically stable types, and studies strict Morley sequences with Kim's lemma and local character.

Findings

Average types of Morley sequences are stationary.

Characterization of generically stable types via eventual types.

Proof of Kim's lemma for strict Morley sequences.

Abstract

We characterize nonforking (Morley) sequences in dependent theories in terms of a generalization of Poizat's special sequences and show that average types of Morley sequences are stationary over their domains. We characterize generically stable types in terms of the structure of the "eventual" type. We then study basic properties of "strict Morley sequences", based on Shelah's notion of strict nonforking. In particular we prove "Kim's lemma" for such sequences, and a weak version of local character.