We prove that every tower of normal filters of height δ (δ supercompact) is precipitous assuming that each normal filter in the tower is the club filter restricted to a stationary set. We give an example to show that this assumption is necessary. We also prove that every normal filter can be generically extended to a well-founded V -ultrafilter (assuming large cardinals). In this paper we inves...

The Connes Embedding Problem (CEP) asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the statement that every type II1 tracial von Neumann algebra has a computable universal theory.

Kirchberg asked in 2004 whether the commutant of L(H) in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter. Let H be a separable infinite dimensional complex Hilbert space, fixed throughout. The purpose of this paper is to prove that, assuming the Continnuum Hypothesis, the commutant of L(H) (the algebra of bo...

We introduce “embedding dimensions” of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II1 factor. These embedding dimensions are von Neumann algebra invariants, i.e., do not depend on the choices of the generators. We also find values of these invariants for some specific von Neumann algebras.

We continue the study started in [2] and characterize j↾V, where j:V[G]→M[H] is an ultrapower embedding by a normal ultrafilter after non-stationary support iteration of Prikry forcings.

In this paper we give an introduction to nonstandard analysis, starting with an ultrapower construction of the hyperreals. We then demonstrate how theorems in standard analysis “transfer over” to nonstandard analysis, and how theorems in standard analysis can be proven using theorems in nonstandard analysis.

This survey is intended primarily for two readerships: general topologists who know a little model theory, and model theorists who know a little general topology. Both camps can boast a healthy constituency, and most of this paper should be readily accessible to anyone in either. The ultraproduct construction has a long and distinguished history. While its beginnings go back to the 1930s with K...

We show how to force distinct values $\mathfrak m$, p$ and h$ the in Cicho?’s diagram, using Boolean Ultrapower method. In our recent paper [J. Math. Logic 21 (2021)] same was done for a newer Maxim

In this paper, we consider ultrapowers of Banach algebras as and the product $${{\bigcirc }_{{(J,\mathcal{U})}}}$$ on second dual algebras. For a algebra A, show that if there is continuous derivation from A into itself, then (A**, ) it. Moreover, X**, where X A-bimodule, ultrapower X; i.e., $${{(X)}_{\mathcal{U}}}$$ . Ultra (character) amenability investigated it will be shown every inner, ult...