Generic expansion and Skolemization in NSOP$_1$ theories
| Autor: | Nicholas Ramsey, Alex Kruckman |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Logic 010102 general mathematics Mathematics - Logic 06 humanities and the arts Function (mathematics) Skolem normal form 03C45 03C10 0603 philosophy ethics and religion 01 natural sciences Quantifier (logic) 060302 philosophy FOS: Mathematics Order (group theory) Algebraic independence 0101 mathematics Special case Constant (mathematics) Logic (math.LO) Mathematics |
| DOI: | 10.48550/arxiv.1706.06616 |
| Popis: | We study expansions of NSOP 1 theories that preserve NSOP 1 . We prove that if T is a model complete NSOP 1 theory eliminating the quantifier ∃ ∞ , then the generic expansion of T by arbitrary constant, function, and relation symbols is still NSOP 1 . We give a detailed analysis of the special case of the theory of the generic L-structure, the model companion of the empty theory in an arbitrary language L. Under the same hypotheses, we show that T may be generically expanded to an NSOP 1 theory with built-in Skolem functions. In order to obtain these results, we establish strengthenings of several properties of Kim-independence in NSOP 1 theories, adding instances of algebraic independence to their conclusions. |
| Databáze: | OpenAIRE |
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