# Sh:759

• Baldwin, J. T., & Shelah, S. (2001). Model companions of T_\mathrm{Aut} for stable T. Notre Dame J. Formal Logic, 42(3), 129–142 (2003).
• 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_{\rm Aut} to have a model companion when T is stable. Namely, we introduce a new condition: T admits obstructions, and show that T_{\rm Aut} has a model companion iff and only if T 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 admits obstructions.
• Current version: 2003-03-13_10 (20p) published version (14p)
Bib entry
@article{Sh:759,
author = {Baldwin, John T. and Shelah, Saharon},
title = {{Model companions of $T_\mathrm{Aut}$ for stable $T$}},
journal = {Notre Dame J. Formal Logic},
fjournal = {Notre Dame Journal of Formal Logic},
volume = {42},
number = {3},
year = {2001},
pages = {129--142 (2003)},
issn = {0029-4527},
mrnumber = {2010177},
mrclass = {03C45},
doi = {10.1305/ndjfl/1063372196},
note = {\href{https://arxiv.org/abs/math/0105136}{arXiv: math/0105136}},
arxiv_number = {math/0105136}
}