Model Companions of T_\sigma for stable T
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 Lautomorphism. 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2001
 arXiv:
 arXiv:math/0105136
 Bibcode:
 2001math......5136B
 Keywords:

 Logic