Model Companions of T_σfor stable T

John Baldwin; Saharon Shelah

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arXiv · math/0105136

Model Companions of T_σfor stable T

John Baldwin·Saharon Shelah

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Abstract

Let T be a complete first order theory in a countable relational language L . We assume relation symbols have been added to make each formula equivalent to a predicate. Adjoin a new unary function symbol sigma to obtain the language L_sigma; T_sigma is obtained by adding axioms asserting that sigma is an L-automorphism. We provide necessary and sufficient conditions for T_sigma to have a model companion when T is stable. Namely, we introduce a new condition: T_sigma admits obstructions, and show that T_sigma has a model companion iff and only if T_sigma does not admit obstructions. This condition is weakening of the finite cover property: if a stable theory T has the finite cover property then T_sigma admits obstructions.

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BibTeX RIS

John Baldwin, Saharon Shelah. 2001-05-16. Model Companions of T_σfor stable T. https://arxiv.org/abs/math/0105136

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