# Sh:312

• Shelah, S. (2017). Existentially closed locally finite groups (Sh312). In Beyond first order model theory, CRC Press, Boca Raton, FL, pp. 221–298.
• Abstract:
We investigate this class of groups originally called ulf (universal locally finite groups) of cardinality \lambda. We prove that for every locally finite group G there is a canonical existentially closed extention of the same cardinality, unique up to isomorphism and increasing with G. Also we get, e.g. existence of complete members (i.e. with no non-inner automorphisms) in many cardinals (provably in ZFC). We also get a parallel to stability theory in the sense of investigating definable types.
• Version 2017-06-09_12 (64p) published version (78p)
Bib entry
@incollection{Sh:312,
author = {Shelah, Saharon},
title = {{Existentially closed locally finite groups (Sh312)}},
booktitle = {{Beyond first order model theory}},
year = {2017},
pages = {221--298},
publisher = {CRC Press, Boca Raton, FL},
mrnumber = {3729328},
mrclass = {03C60 (03C45)},
note = {\href{https://arxiv.org/abs/1102.5578}{arXiv: 1102.5578}},
arxiv_number = {1102.5578}
}