Submission date: 27 October 2012.

Abstract:

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) [7], [9]. 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 [6] identifying extremely amenable groups with the automorphism groups of limits of Ramsey classes.

Mathematics Subject Classification: 03C52, 05C55

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Full text arXiv 1210.7373: pdf, ps.