Sh:977

• Shelah, S. (2012). Modules and infinitary logics. In Groups and model theory, Vol. 576, Amer. Math. Soc., Providence, RI, pp. 305–316. arXiv: 1011.3581 DOI: 10.1090/conm/576/11376 MR: 2962893
• Abstract:
  We deal with Abelian groups and R-modules. We consider theories in infinitary logic of the form \mathbb{L}_{\lambda,\theta} of such structures M and prove they have elimination of quantifiers up to filtered existential universal formulas, (so ones defining subgroups of some power of M). Hence those theories are stable in the appropriate sense and understood to some extent.

  We thank John Baldwin, in 2026, raised some issues with this work. For the details, see the introduction.

• Version 2026-08-24_3 (2p) published version (12p)

@incollection{Sh:977,
 author = {Shelah, Saharon},
 title = {{Modules and infinitary logics}},
 booktitle = {{Groups and model theory}},
 series = {Contemp. Math.},
 volume = {576},
 year = {2012},
 pages = {305--316},
 publisher = {Amer. Math. Soc., Providence, RI},
 mrnumber = {2962893},
 mrclass = {03C60 (03C10 03C45 03C75 16B70)},
 doi = {10.1090/conm/576/11376},
 note = {\href{https://arxiv.org/abs/1011.3581}{arXiv: 1011.3581}},
 arxiv_number = {1011.3581}
}