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Preprint Number 524
524. Cameron Donnay Hill
Generalized Indiscernibles as Model-complete Theories
Submission date: 27 October 2012.
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) , . We understand theories of indiscernibles to be special kinds of companionable theories of finite structures, and much of the work in our arguments is carried in the context of the model-companion. Among other things, this approach allows us to prove that the companion of a theory of indiscernibles whose base consists of the quantifier-free formulas is necessarily the theory of the Fraisse limit of a Fraisse class of linearly ordered finite structures (where the linear order will be at least quantifier-free definable). We also provide streamlined arguments for the result of  identifying extremely amenable groups with the automorphism groups of limits of Ramsey classes.
Mathematics Subject Classification: 03C52, 05C55
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