Related papers: More on regular reduced products
We continue the research of the relation $\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ on the set $\beta {\mathbb{N}}$ of ultrafilters on ${\mathbb{N}}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as…
We construct non-isomorphic models M, N, e.g. of cardinality aleph_1 such that in the Ehrenfeucht-Fraisse game of length zeta < omega_1 the isomorphism player wins
Let C denote any of the following cardinal characteristics of Boolean algebras: incomparability, spread, character, pi-character, hereditary Lindelof number, hereditary density. It is shown to be consistent that there exists a sequence…
Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between $\Pi^1_2$ principles over $\omega$-models of…
Two structures A and B are n-equivalent if player II has a winning strategy in the n-move Ehrenfeucht-Fraisse game on A and B. We extend earlier results about n-equivalence for finite coloured linear orders, describing an algorithm for…
We present two different types of models where, for certain singular cardinals lambda of uncountable cofinality, lambda -> (lambda, omega+1)^2, although lambda is not a strong limit cardinal. We announce, here, and will present in a…
It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if…
We show that if $\lambda^{<\kappa} = \lambda$ and every normal filter on $P_\kappa\lambda$ can be extended to a $\kappa$-complete ultrafilter then so does every $\kappa$-complete filter on $\lambda$. This answers a question of Gitik.
Let lambda be an infinite cardinal number and let C = {H_i| i in I} be a family of nontrivial groups. Assume that |I|<=lambda, |H_i|<= lambda, for i in I, and at least one member of C achieves the cardinality lambda. We show that there…
We discuss the connection between various orders on the class of all the ultrafilters and certain compactness properties of abstract logics and of topological spaces. We present a model theoretical characterization of Comfort order. We…
We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraisse games between a fixed group of cardinality lambda and a free Abelian group. A group is called epsilon-game-free if the isomorphism…
In this paper, we study equality-type Clarke subdifferential chain rules of matrix factorization and factorization machine. Specifically, we show for these problems that provided the latent dimension is larger than some multiple of the…
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as…
In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the…
We complete the characterization of the possible spectrum of regular ultrafilters D on a set I, where the spectrum is the set of infinite cardinals which are ultraproducts of finite cardinals modulo D.
We give the first (ZFC) dividing line in Keisler's order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal $\lambda$ for which there is $\mu < \lambda \leq 2^\mu$, we construct…
Suppose that lambda is the successor of a singular cardinal mu whose cofinality is an uncountable cardinal kappa. We give a sufficient condition that the club filter of lambda concentrating on the points of cofinality kappa is not…
The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…
An infinite cardinal $\lambda$ is called Fr\'echet if the Fr\'echet filter on $\lambda$ extends to a countably complete ultrafilter. We investigate the relationship between Fr\'echet cardinals and strongly compact cardinals under a…
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…