Related papers: Brouwer and Cardinalities

We prove combinatorial theorems concerning the stick principle and cardinal characteristics.

This paper studies cardinal invariants b_kappa and t_kappa, the natural generalizations of the invariants b and t to a regular cardinal kappa.

We study the cardinality of the set of manifolds homotopy equivalent to a given manifold M and compare it to the cardinality of the structure set of M.

The paper deals with continuous solutions of a Schilling's problem.

This paper is intended to survey the basics of localization and anti-localization cardinals on the reals, and its interplay with notions and cardinal characteristics related to measure and category.

C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are…

I review the present state of knowledge concerning transversity distributions and related observables. In particular, I discuss the phenomenology of transverse asymmetries in e p\uparrow, p p\uparrow, p\uparrow p\uparrow and pbar \uparrow…

We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.

This paper develops a rich theory of cardinality in the paraconsistent and paracomplete set theory $\mathrm{BZFC}$, where sets can be inconsistent ($A$ such that ``$x\in A$'' is both true and false for some $x$) or incomplete ($A$ such that…

The main result of this paper is Theorem. For every integer $d\geqslant 2$ the set of biLipschitz classes in $\mathbb{E}^d$ has cardinality continuum.

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

We prove that any definable family of subsets of a definable infinite set $A$ in an o-minimal structure has cardinality at most $|A|$. We derive some consequences in terms of counting definable types and existence of definable topological…

If the Continuum Hypothesis is false, it implies the existence of cardinalities between the integers and the real numbers. In studying these "cardinal characteristics of the continuum", it was discovered that many of the associated…

The paper proves a conjecture of Solomon Feferman concerning the indefiniteness of the continuum hypothesis relative to a semi-intuitionistic set theory.

We give a partial answer to a conjecture of A. Balog, concerning the size of AA+A, where A is a finite subset of real numbers. Also, we prove several new results on the cardinality of A:A+A, AA+AA and A:A + A:A.

We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.

The research in this paper is a continuation of the investigation of the cardinality of the $\theta$-closed hull of subsets of spaces. This research obtains new upper bounds of the cardinality of the $\theta$-closed hull of subsets using…

Every conditionally convergent series of real numbers has a divergent subseries. How many subsets of the natural numbers are needed so that every conditionally convergent series diverges on the subseries corresponding to one of these sets?…

We extend Freiman's inequality on the cardinality of the sumset of a $d$ dimensional set. We consider different sets related by an inclusion of their convex hull, and one of them added possibly several times.

We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion…