Sh:1098

• Shelah, S. (2023). Lf groups, aec amalgamation, few automorphisms. In Beyond first order model theory. Vol. II, CRC Press, Boca Raton, FL, pp. 141–173. arXiv: 1901.09747 MR: 4920852
• Abstract:
  We deal mainly with \mathbf{K} ^{\rm lf}_\lambda, the class of locally finite groups of cardinality \lambda, in particular \mathbf{K} ^{\rm exlf}_\lambda, the class of existentially closed locally finite groups. In §3 we prove that for almost every cardinal \lambda “every locally finite group G of cardinality \lambda can be extended to an existentially closed complete group of cardinality \lambda which moreover is so called (\lambda,\theta)-full; note that §3 which do not rely on §1,§2. (in earlier results G has cardinality < \lambda and also \lambda was restricted).

  In §1 we deal with amalgamation bases, for the class of lf (= locally finite) groups, and general suitable classes, we define when it has the (\lambda,\kappa)-amalgamation property which means that “many" models M \in K^{\mathfrak{k} }_\lambda are amalgamation bases and get more than expected. In this case, we deal with a general frame - so called a.e.c., abstract elementary class. In §2 we deal with weak definability of a \in N \backslash M over M, for = existentially closed {\rm lf} group.

• Version 2020-02-17_4 (27p)

@incollection{Sh:1098,
 author = {Shelah, Saharon},
 title = {{Lf groups, aec amalgamation, few automorphisms}},
 booktitle = {{Beyond first order model theory. Vol. II}},
 year = {2023},
 pages = {141--173},
 publisher = {CRC Press, Boca Raton, FL},
 mrnumber = {4920852},
 mrclass = {03C55 (03C50 03C60)},
 note = {\href{https://arxiv.org/abs/1901.09747}{arXiv: 1901.09747}},
 arxiv_number = {1901.09747}
}