Related papers: Rapid ultrafilters and summable ideals

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. It is shown…

Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m_R. We consider multiplicities and mixed multiplicities of R by filtrations of m_R-primary ideals. We show that the theorem of Teissier, Rees and…

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

Within an axiomatic framework, we prove that the existence of faster than light particles is consistent with (does not contradict) the dynamics of Einstein's special relativity.

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

Let $(S,\cdot)$ be a semigroup and $\mathfrak{m}$ be a $\sigma$-algebra on $S$. We say $(S,\cdot,\mathfrak{m})$ is a measurable semigroup if $\pi:S\times S\longrightarrow S$ by $\pi(x,y)=x\cdot y$ is a measurable function. In this paper ,…

Some new results concerning the equation $\sigma(N)=aM, \sigma(M)=bN$ are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.

We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong…

We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously…

We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.

Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small…

In earlier work of the second and third author the equivalence of a finite square principle square^fin_{lambda,D} with various model theoretic properties of structures of size lambda and regular ultrafilters was established. In this paper…

It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom of Choice than traditional elementary analysis. The claim is based on the observation that the hyperreals entail the existence of nonprincipal…

Problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attraction sets are constructed.

We characterize some classes of finite soluble groups. In particular, we prove that: a finite group $G$ is supersoluble if and only if $G$ has a normal subgroup $D$ such that $G/D$ is supersoluble and $D$ avoids every chief factor of $G$…

We investigate which filters on $\omega$ can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in $[\omega]^\omega$). We prove the following results: - Many classical examples of nice tall filters…

Suppose $I$ is an ideal of a polynomial ring over a field, $I\subseteq k[x_1,\ldots,x_n]$, and whenever $fg\in I$ with degree $\leq b$, then either $f\in I$ or $g\in I$. When $b$ is sufficiently large, it follows that $I$ is prime.…

We study the structure of the Rudin-Frolik order on countably complete ultrafilters under the assumption that this order is directed. This assumption, called the Ultrapower Axiom, holds in all known canonical inner models. It turns out that…

The relationship between the large cardinal notions of strong compactness and supercompactness cannot be determined under the standard ZFC axioms of set theory. Under a hypothesis called the Ultrapower Axiom, we prove that the notions are…

We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and…