A dichotomy for $D$-rank 1 types in simple theories
Logic
2019-09-20 v3
Abstract
We prove a dichotomy for -rank 1 types in simple theories that generalizes Buechler's dichotomy for -rank 1 minimal types in stable theories: every -rank 1 type is either 1-based or part of its algebraic closure, defined by a single formula, almost contains a non-algebraic formula that belongs to a non-forking extension of the type. In addition we prove that a densely 1-based type of -rank 1 is 1-based. We also observe that for a hypersimple unidimensional theory the existence of a non-algebraic stable type implies stability (and thus superstability).
Keywords
Cite
@article{arxiv.1311.4053,
title = {A dichotomy for $D$-rank 1 types in simple theories},
author = {Ziv Shami},
journal= {arXiv preprint arXiv:1311.4053},
year = {2019}
}
Comments
Minor correction made in the statement and proof of Corollary 3.21