We develop the method of iterated ultrapower representation to provide a unified and perspicuous approach for building automorphisms of countable recursively saturated models of Peano arithmetic PA. In particular, we use this method to prove Theorem A below, which confirms a long standing conjecture of James Schmerl. Theorem A. If M is a countable recursively saturated model of PA in which N is...

Associated to each ultrafilter U on ω and each map p : ω → ω is a Dedekind cut in the ultrapower ω/p(U). Blass has characterized, under CH, the cuts obtainable when U is taken to be either a p-point ultrafilter, a weakly-Ramsey ultrafilter or a Ramsey ultrafilter. Dobrinen and Todorcevic have introduced the topological Ramsey spaceR1. Associated to the spaceR1 is a notion of Ramsey ultrafilter ...

In this paper we show that the core model might exist even if there are Woodin cardinals in V . This observation is not new. Woodin [8], in his proof that ADR implies the ADR hypothesis, constructed models of ZFC in which there are fully iterable extender models with Woodin cardinals which satisfy (among other things) a weak covering property. Steel [7], in his proof that Mn satisfies V = HOD, ...

This article investigates the representative-agent hypothesis for a population which faces a collective choice from a given finite-dimensional space of alternatives. Each individual’s preference ordering is assumed to admit a utility representaion through an element of an exogenously given set of admissible utility functions. In addition, we assume that (i) the class of admissible utility funct...

We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever X̂ is an ultrapower of X and B is a ball in X̂, the intersection B ∩X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B,...

We prove the statement in the title.

We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...

Let 91 be a ~-complete ultrafilter on the measurable cardinal ~. Scott [ 1 3 ] proved V ¢ L by using 91 to take the ultrapower of V. Gaifman [ 2] considered iterated ultrapowers of V by cg to conclude even stronger results; for example, that L n ~(6o) is count-able. In this paper we discuss some new applications of iterated ultra-powers. In § § 1-4, we develop a straightforward generalization o...

In this paper I propose the non-Archimedean multiple-validity. Further, I build an infinite-order predicate logical language in that predicates of various order are considered as fuzzy relations. Such a language can have non-Archimedean valued semantics. For instance, infinite-order predicates can have an interpretation in the set [0, 1] of hyperreal (hyperrational) numbers. Notice that there e...

Associated to each ultrafilter U on ω and each map p : ω → ω is a Dedekind cut in the ultrapower ωω/p(U). Blass has characterized, under CH, the cuts obtainable when U is taken to be either a p-point ultrafilter, a weakly-Ramsey ultrafilter or a Ramsey ultrafilter. Dobrinen and Todorcevic have introduced the topological Ramsey space R1. Associated to the space R1 is a notion of Ramsey ultrafilt...