Existentially closed locally finite groups

by Shelah. [Sh:312]

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.

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