Classification over a predicate -- the general case. Part I -- structure theory
Logic
2023-02-17 v2
Abstract
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an independence notion and explore its properties, prove stable amalgamation results, and show that every type over a model, orthogonal to the predicate, is generically stable.
Cite
@article{arxiv.1910.10811,
title = {Classification over a predicate -- the general case. Part I -- structure theory},
author = {Saharon Shelah and Alexander Usvyatsov},
journal= {arXiv preprint arXiv:1910.10811},
year = {2023}
}