Related papers: On the bounding, splitting, and distributivity num…

A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…

The main result of this paper is the proof of the simultaneous consistency, modulo a weakly compact cardinal, of the equality $2^{< \mathfrak{c}} = \mathfrak{c}$ with the following property (*) of partitions of pairs of $\mathfrak{c}$:…

For g < f in omega^omega we define c(f,g) be the least number of uniform trees with g-splitting needed to cover a uniform tree with f-splitting. We show that we can simultaneously force aleph_1 many different values for different functions…

Given a Banach space we consider the $\sigma$-ideal of all of its subsets which are covered by countably many hyperplanes and investigate its standard cardinal characteristics as the additivity, the covering number, the uniformity, the…

The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question here is if there is, in ZFC, a regular (or just Hausdorff) SP…

Let $F_h(n)$ denote the minimum cardinality of an additive {\em $h$-fold basis} of $\{1,2,\cdots,n\}$: a set $S$ such that any integer in $\{1,2,\cdots, n\}$ can be written as a sum of at most $h$ elements from $S$. While the trivial bounds…

We show that, when $sp>N$, the sharp Hardy constant $\mathfrak{h}_{s,p}$ of the punctured space $\mathbb R^N\setminus\{0\}$ in the Sobolev-Slobodecki\u{\i} space provides an optimal lower bound for the Hardy constant…

This is a revised version (of late 2020) of [Sh:700], which is arXiv:math/0012170 . First point is noting that the proof of Theorem 4.3 in [Sh:700], which says that the proof giving the consistency $ \mathfrak{b} = \mathfrak{d} =…

Assuming $\mathfrak b = \mathfrak c$ (or some weaker statement), we construct a compactification $\gamma\omega$ of $\omega$ such that its remainder $\gamma\omega\setminus\omega$ is nonseparable and carries a strictly positive measure.

We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer $d$ there is a constant $c_d > 0$ such that whenever $X_1,..., X_{d+1}$ are $n$-element subsets of $\mathbb{R}^d$, then we…

We continue the study from \cite{BrendleFreidmanMontoya, vandervlugtlocalizationcardinals} of localization cardinals $\mfb_\kappa(\in^*)$ and $\mfd_\kappa(\in^*)$ and their variants at regular uncountable $\kappa$. We prove that if $\kappa$…

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…

We investigate a family of relational systems arising from interval partitions of $\omega$, inspired by Vojt\'a\v{s}'s characterization of the bounding and dominating numbers. By varying the underlying asymptotic quantifiers and interval…

Based on the well-known cardinal characteristics $\mathfrak{s}$, $\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection…

We prove the consistency of: for suitable strongly inaccessible cardinal lambda the dominating number, i.e., the cofinality of ^{lambda}lambda, is strictly bigger than cov_lambda(meagre), i.e. the minimal number of nowhere dense subsets of…

Let $C\subseteq \{1,\ldots,k\}^n$ be such that for any $k$ distinct elements of $C$ there exists a coordinate where they all differ simultaneously. Fredman and Koml\'os studied upper and lower bounds on the largest cardinality of such a set…

In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$…

We answer a question from Raghavan and Stepr{\=a}ns' paper on weakly tight families by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under…

Much recent work in cardinal characteristics has focused on generalizing results about $\omega$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$…

In this article we investigate the dual-shattering cardinal H, the dual-splitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (the shattering cardinal, also known as the distributivity…