We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no ultrafilter ...

There are many papers in the literature that discuss the asymptotic fixed point theory, in which the existence of the fixed points is deduced from the assumption on the iterates of an operator (e.g., [1, 6] and the references therein). Recently, Kirk [5] studied an asymptotic fixed point theorem concerning nonlinear contractions. He proved the following theorem [5, Theorem 2.1] by appealing to ...

Suppose D is an ultrafilter on κ and λ = λ. We prove that if Bi is a Boolean algebra for every i < κ and λ bounds the Depth of every Bi, then the Depth of the ultraproduct of the Bi’s mod D is bounded by λ. We also show that for singular cardinals with small cofinality, there is no gap at all. This gives a partial answer to problem No. 12 in [?]. 2000 Mathematics Subject Classification. Primary...

3 Construction of Star Types Using Ultrafilters 14 3.1 A Free Ultrafilter over the Naturals . . . . . . . . . . . . . . . 15 3.2 Definition of star type constructor . . . . . . . . . . . . . . . 15 3.3 Transfer principle . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Standard elements . . . . . . . . . . . . . . . . . . . . . . . . 17 3.5 Internal functions . . . . . . . . . . . . . ....

___________ _ A high flux, non-traumatic ultrafilter (UF) can be useful for co;Jtrolling the volume in the cardiopulmonary bypass circuit. Recently three such devices have been made available. It is the purpose of this work to describe the direct effects of ultrafiltration with one of these devices, the HemoConcentrator, on blood. The effects were determined by calculating the net changes in bl...

This paper develops a new approach to the analysis of the underlying power structure when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness, which is weaker than standard decisiveness, and investigate the family of quasi-decisive groups associated an Arrovian collective choice rule. A group is quasi-decisive if for every pair x, y of alternatives, y i...

We force the existence of a non-trivial κ \kappa -complete ultrafilter over which fails to satisfy Galvin prop...

Motivated by Tukey classification problems and building on work in Part 1 [5], we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [7], and for each α < ω1, Rα+1 coming immediately after Rα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a ...

We prove a number of results motivated by global questions of uniformity in recursion theory, and some longstanding open questions about universality of countable Borel equivalence relations. Our main technical tool is a class of games for constructing functions on free products of countable groups. These games show the existence of refinements of Martin’s ultrafilter on Turing invariant sets t...