Disassociated indiscernibles

Generalized 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...

A Dependent Theory with Few Indiscernibles

Indiscernibles and dimensional compactness

Abstract. This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set uS ⊆ G in a biequivalence vector space 〈W,M,G〉, such that x − y / ∈ M for distinct x, y ∈ u, contains an infinite independent subset. Consequently, a class X ⊆ G is dimensionally compact iff the π-equivalence . ...

Dropping cofinalities

Our aim is to present constructions in which some of the cofinalities drop down, i.e. the generators of PCF structure are far a part. 1 Some Preliminary Settings Let λ0 < κ0 < λ1 < κ1 < ... < λn < κn < ...., n < ω be a sequence of cardinals such that for each n < ω • λn is λ +n+2 n +2 n strong as witnessed by an extender Eλn • κn is κ +n+2 n +2 n strong as witnessed by an extender Eκn Let κ = ⋃...

1 Independence Structures in Set Theory

The axioms for "independent choices" presented in van Lambalgen [1992] are strengthened here, so that they can be seen as introducing a new type of indiscernibles in set theory. The resulting system allows for the construction of natural inner models. The article is organised as follows. Section 1 introduces the axioms, some preliminary lemmas are proved and the relation with the axiom of choic...