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arXiv · 1910.10811

Classification over a predicate -- the general case. Part I -- structure theory

Saharon Shelah·Alexander Usvyatsov
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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.

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BibTeXRIS

Saharon Shelah, Alexander Usvyatsov. 2019-10-23. Classification over a predicate -- the general case. Part I -- structure theory. https://arxiv.org/abs/1910.10811

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