### 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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