Sh:322a

• Shelah, S., & Usvyatsov, A. Classification over a predicate — the general case I. J of Math Logic. To appear. 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)

@article{Sh:322a,
 author = {Shelah, Saharon and Usvyatsov, Alexander},
 title = {{Classification over a predicate --- the general case I}},
 journal = {J of Math Logic},
 year = {to appear},
 note = {\href{https://arxiv.org/abs/1910.10811}{arXiv: 1910.10811}},
 arxiv_number = {1910.10811}
}