# Sh:322a

• Shelah, S., & Usvyatsov, A. Classification over a predicate — the general case I. Preprint. arXiv: 1910.10811
• Abstract:
We begin systematic development of structure theory for a first order theory stable over a monadic predicate. We show that stability over a predicate implies quantrifier 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.
• Version 2023-02-16_2 (34p)
Bib entry
@article{Sh:322a,
author = {Shelah, Saharon and Usvyatsov, Alexander},
title = {{Classification over a predicate --- the general case I}},
note = {\href{https://arxiv.org/abs/1910.10811}{arXiv: 1910.10811}},
arxiv_number = {1910.10811}
}