Submission date: 19 April 2018

Abstract:

We introduce notions of stationary ordered types and theories; the latter generalizes weakly quasi-o-minimality. We show that in that context forking as a binary relation is an equivalence relation and that each stationary ordered type in a model determines some order-type as an invariant of the model. We prove that invariants of a model that correspond to distinct types behave well when the types are non-orthogonal. The developed techniques are applied to prove that in the case of a binary, stationary ordered theory with fewer than 2^{ℵ_0} countable models, the isomorphism type of a countable model is determined by a certain sequence of order-types (invariants of the model). In particular, we prove Vaught's conjecture for binary, stationary ordered theories.

Mathematics Subject Classification: 03C15, 03C45, 03C64

Keywords and phrases:

Full text arXiv 1804.07231: pdf, ps).