Model companions of taut for stable t

John T. Baldwin; Saharon Shelah

doi:10.1305/ndjfl/1063372196

Model companions of t_aut for stable t

John T. Baldwin^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory T_Aut by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if T_Aut has a model companion. The proof involves some interesting new consequences of the nfcp.

Original language	English
Pages (from-to)	129-140
Number of pages	12
Journal	Notre Dame Journal of Formal Logic
Volume	42
Issue number	3
DOIs	https://doi.org/10.1305/ndjfl/1063372196
State	Published - 2001

Keywords

Expansion by automorphism
Stability

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10.1305/ndjfl/1063372196

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abstract = "We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory TAut by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if TAut has a model companion. The proof involves some interesting new consequences of the nfcp.",

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AU - Shelah, Saharon

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AB - We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory TAut by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if TAut has a model companion. The proof involves some interesting new consequences of the nfcp.

KW - Expansion by automorphism

KW - Stability

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Model companions of t_aut for stable t

Abstract

Keywords

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