Related papers: On regular reduced products

We construct a model of the form $L[A,U]$ that exhibits the simplest structural behavior of $\sigma$-complete ultrafilters in a model of set theory with a single measurable cardinal $\kappa$ , yet satisfies $2^\kappa = \kappa^{++}$. This…

When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…

This note concerns bounded derivations on maximal triangular operator algebras on a Hilbert space. Given any bounded derivation $\delta$ on a maximal triangular algebra whose invariant lattice is continuous at 1, an operator which is shown…

One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…

Let K^0_lambda be the class of structures < lambda,<,A>, where A subseteq lambda is disjoint from a club, and let K^1_lambda be the class of structures < lambda,<,A>, where A subseteq lambda contains a club. We prove that if lambda =…

Given two symmetric and positive semidefinite square matrices $A, B$, is it true that any matrix given as the product of $m$ copies of $A$ and $n$ copies of $B$ in a particular sequence must be dominated in the spectral norm by the ordered…

We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to…

We study correspondences of tracial von Neumann algebras from the model-theoretic point of view. We introduce and study an ultraproduct of correspondences and use this ultraproduct to prove, for a fixed pair of tracial von Neumann algebras…

Embedding based models have been the state of the art in collaborative filtering for over a decade. Traditionally, the dot product or higher order equivalents have been used to combine two or more embeddings, e.g., most notably in matrix…

We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption…

In this paper we study conditions under which, for an inclusion of finite von Neumann algebras $N \subseteq M$, we have the reduced amalgamated free product $\ast_N M$ is embeddable into $(R \bar{\otimes} N_1)^\omega$ for some other finite…

As children acquire the knowledge of their language's morphology, they invariably discover the productive processes that can generalize to new words. Morphological learning is made challenging by the fact that even fully productive rules…

The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…

Let $\kappa,\lambda$ be regular cardinals, $\lambda\le\kappa$, let $\varphi$ be a sentence of the language $\mathcal L_{\kappa,\lambda}$ in a given signature, and let $\vartheta(\varphi)$ express the fact that $\varphi$ holds in a submodel,…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer $M_1^{\varphi_1}$ is diffuse. We first show that any…

We generalize the results from "P. Lipparini, Productive $[\lambda,\mu]$-compactness and regular ultrafilters, Topology Proceedings, 21 (1996), 161--171"; in particular the present results apply to singular cardinals, too.

This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call \emph{Welch games}. Player II having a winning strategy in the Welch game of length $\omega$ on $\kappa$ is…

We develop a unified framework for iterated symmetric extensions with countable support and, more generally, with $<\kappa$-support. Set-length iterations are treated uniformly, and when the iteration template is first-order definable over…

There has been much interest on constructing models which are not isomorphic of cardinality lambda but are equivalent under the Ehrenfeucht-Fraisse game of length alpha even for every alpha<lambda. So under G.C.H. we know much. We deal here…

Let $V(\lambda)$ be the irreducible lowest weight $U_q(D(N,1))$-module with lowest weight $\lambda$. Assume $\lambda = n_0\omega_0-\sum_{i=0}^{N}n_i\omega_i$, where $\omega_0$ is the fundamental weight corresponding to the unique odd coroot…