2001/05/16 by John Baldwin, John T. Baldwin, Saharon Shelah +2
Computer Science · Mathematics · #FOS: Mathematics #Logic (math.LO) #Polynomial and algebraic computation #math.LO
paper · pdf · doi:10.48550/arxiv.math/0105136
published as Notre Dame J. Formal Logic 42 No. 3 (2001) 129--142 (2003)
arxiv created 2001/05/16 · openalex publication_date 2001/05/16 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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 Lsigma; Tsigma is obtained by adding axioms asserting that sigma is an L-automorphism. We provide necessary and sufficient conditions for Tsigma to have a model companion when T is stable. Namely, we introduce a new condition: Tsigma admits obstructions, and show that Tsigma has a model companion iff and only if Tsigma does not admit obstructions. This condition is weakening of the finite cover property: if a stable theory T has the finite cover property then Tsigma admits obstructions.