Universales indiscernibles

Disassociated indiscernibles

This work defines a variant of Prikry forcing and applies it to increase the number of normal measures on a single cardinal, relying on a large cardinal property of consistency strength between measurable and Mitchell order two. In particular, from an assumption weaker than o(κ) = 2, there is a forcing extension in which the first measurable cardinal κ has any number λ ≤ κ of normal measures.

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 . ...

Models Without Indiscernibles

For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size 2, with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least 2, (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly 2b,.) If TX true arithmetic, then H(T) = 2,. If 8 -A (p)'-, then any complet...

A Dependent Theory with Few 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...