We construct a model of ZF in which there is a measurable cardinal but there is no normal ultrafilter over it.

Let $\mathcal E$ be the $\sigma $-ideal generated by closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration ccc posets to force that, for E$, their associated cardinal characteristics (i.e. additivity, coveri

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

Sterile single-use ultrafilters are used in dialysis for the preparation of the substitution fluid given to patients undergoing dialysis treatments with high convective fluid removal. The retention of pyrogenic agents by the ultrafilters is crucial to avoiding inflammatory responses. The performance of a new single-use ultrafilter (NUF) with a positively charged flat sheet membrane of relativel...

This document provides solutions to the exercises in “Iterated Ultrapowers for the Masses”. 3.3. Exercise. Let U be anM-amenable ultrafilter on the parametricallyM-definable subsets of M . We begin by showing that U2 is a filter on the parametricallyM-definable subsets of M2. Let X,Y ⊆M2 be parametrically M-definable. Let Z = {m ∈M : (X ∩ Y )|m ∈ U}, Z1 = {m ∈M : X|m ∈ U}, Z2 = {m ∈M : Y |m ∈ U...