# 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. - 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}, doi = {10.1305/ndjfl/1063372196}, mrclass = {03C45}, mrnumber = {2010177}, mrreviewer = {Carlo Toffalori}, doi = {10.1305/ndjfl/1063372196}, note = {\href{https://arxiv.org/abs/math/0105136}{arXiv: math/0105136}}, arxiv_number = {math/0105136} }