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). arXiv: math/0105136 DOI: 10.1305/ndjfl/1063372196 MR: 2010177
• 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.
• Version 2003-03-13_11 (20p) published version (14p)

@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}
}