Dimension and simplicity for Ramsey-expandable classes of finite structures
نویسنده
چکیده
We introduce a notion of manufactured dimension function (with values in R∪{−∞}) for the generic model of a Ramsey-expandable class of finite structures. This idea allows us to extract an automorphism-invariant dimension from a Hrushovski-style psuedo-finite dimension function as presented in [12, 13]. Adapting the technique of [6], we demonstrate that the existence of a manufactured dimension function whose image is well-ordered is sufficient for super-simplicity. Further, we show that the generic model of a Ramsey-expandable class whose generic theory has the finite sub-model property always admits a manufactured dimension function (possibly not well-ordered). Finally, we formulate some conjectures around well-ordering and simplicity of the generic theory of a Ramsey-expandable class that suggest a possible approach to showing that the theory of the Henson graph is not pseudo-finite.
منابع مشابه
New Ramsey Classes from Old
Let C1 and C2 be strong amalgamation classes of finite structures, with disjoint finite signatures σ and τ . Then C1∧C2 denotes the class of all finite (σ∪τ)-structures whose σ-reduct is from C1 and whose τ -reduct is from C2. We prove that when C1 and C2 are Ramsey, then C1 ∧ C2 is also Ramsey. We also discuss variations of this statement, and give several examples of new Ramsey classes derive...
متن کاملAll those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
We prove the Ramsey property of classes of ordered structures with closures and given local properties. This generalises earlier results: the Nešetřil-Rödl Theorem, the Ramsey property of partial orders and metric spaces as well as the author’s Ramsey lift of bowtiefree graphs. We use this framework to give new examples of Ramsey classes. Among others, we show (and characterise) the Ramsey prop...
متن کاملRamsey properties and extending partial automorphisms for classes of finite structures
We show that every free amalgamation class of finite structures with relations and (symmetric) partial functions is a Ramsey class when enriched by a free linear ordering of vertices. This is a common strengthening of the Nešetřil-Rödl Theorem and the second and third authors’ Ramsey theorem for finite models (that is, structures with both relations and functions). We also find subclasses with ...
متن کاملTopological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points
We present a general method for constructing a new class of topological Ramsey spaces. Members of such spaces are infinite sequences of products of Fräıssé classes of finite relational structures satisfying the Ramsey property. We extend the Product Ramsey Theorem of Sokič to equivalence relations for finite products of structures from Fräıssé classes of finite relational structures satisfying ...
متن کاملGeneralized Indiscernibles as Model-complete Theories
We define a mild generalization of classical Fraïssé classes, and in this context, we recover several old (often with novel proofs) and new facts about Ramsey classes and generalized indiscernibles in the sense of [12], [17], and other sources. Of particular novelty are: (1) a new and clearly model-theoretic proof of the equivalence of the Ramsey property and the extreme amenability of the auto...
متن کامل