Related papers: Remarks on the intersection of filters

In this paper we construct examples of irrational behavior of multiplicities and mixed multiplicities of divisorial filtrations. The construction makes essential use of anti-positive intersection products.

We show that large scale oscillons, i.e., quasi-periodic, long living particle like solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takes into account nonlinear…

We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly…

We address a system of weakly interacting particles where the heterogenous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers…

We show that there exist unbounded functionals on the spaces of sequences that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint.

Guo and Xu determined the maximum size of intersecting families over finite affine spaces and showed that any family reaches maximum size must be trivial. In this paper, we characterize non-trivial intersecting family with maximum size.

We construct a non-elementary Fuchsian group that admits two non-elementary subgroups with trivial intersection and whose radial limit sets intersect non-trivially. This negatively answers a question of Perry Susskind (1989) that was stated…

Let $ k, n \in \mathbb{N}^+ $ and $ m \in \mathbb{N}^+ \cup \{\infty \} $. A $ k $-multiset in $ [n]_m $ is a $ k $-set whose elements are integers from $ \{1, 2, \ldots, n\} $, and each element is allowed to have at most $ m $ repetitions.…

We show that there exist closed manifolds with arbitrarily small transcendental simplicial volumes. Moreover, we exhibit an explicit uncountable family of (transcendental) real numbers that are not realised as the simplicial volume of a…

We prove the consistency of ZF+DC+"there are no mad families"+"there exists a non-meager filter on $\omega$" relative to ZFC, answering a question of Neeman and Norwood. We also introduce a weaker version of madness, and we strengthen the…

Let $n=2k+1$ be odd with $k\geq3$. In this note, we give two intersecting families with diversity larger than $\sum_{i=k+1}^{2k} \binom {2k}{i}$, which disprove a conjecture of Huang.

Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.

A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a…

We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. This shows the "Strong Dirac" conjecture to be false for pseudolines. We…

A union ultrafilter is an ultrafilter over the finite subsets of $\omega$ that has a base of sets of the form $\mathrm{FU}(X)$, where $X$ is an infinite pairwise disjoint family and $\mathrm{FU}(X)=\{\bigcup…

This is a reminder that an infinite series can be defined other than as the limit of a sequence of finite series. An example is provided in which a circuit element comprised of an infinite series of resistors has negative resistance.

The quantum marginal problem is concerned with characterizing which collections of quantum states on different subsystems are compatible in the sense that they are the marginals of some multipartite quantum state. Presented here is a…

The Suslin hypothesis states that there are no nonseparable complete dense linear orderings without endpoints which have the countable chain condition. $\mathsf{ZF + AD^+ + V = L(\mathscr{P}(\mathbb{R}))}$ proves the Suslin hypothesis. In…

In this paper we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over selection principles of the type U_fin(O,A).

Definable stationary sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily ordinal definable sets. Fixing a certain notion of…