Related papers: Reductions Between Cardinal Characteristics of the…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
We prove that consistently, cov($\mathcal{M})< \lambda_\mathbf{0} < \lambda_\mathbf{1} < \lambda_\mathbf{\infty} < 2^{\aleph_0}$, where $\lambda_\mathbf{0}$ denotes the weak Borel chromatic number of the Kechris-Solecki-Todor\v{c}evi\'c…
A $k$-connected set in an infinite graph, where $k > 0$ is an integer, is a set of vertices such that any two of its subsets of the same size $\ell \leq k$ can be connected by $\ell$ disjoint paths in the whole graph. We characterise the…
We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of…
As is well known, the "usual discrepancy" is defined for a normal Q-Gorenstein variety. By using this discrepancy we can define a canonical singularity and a log canonical singularity. In the same way, by using a new notion, Mather-Jacobian…
We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\bbC\setminus E$ is a domain of Widom type with the Direct Cauchy Theorem we give an explicit…
This is a part of an ongoing research project, with the aim of finding the connections between properties related to theory combination in Satisfiability Modulo Theories. In previous work, 7 properties were analyzed: convexity, stable…
The first step to study lower bounds for a stochastic process is to prove a special property - Sudakov minoration. The property means that if a certain number of points from the index set are well separated then we can provide an optimal…
Let "ex" be the cardinality of the smallest independent family of subsets of omega (independent means that all nontrivial Boolean combinations are infinite) which cannot be extended to a homogeneous independent family. "Homogeneous" means…
Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.
We prove that the Gauss curvature and the curvature of the normal connection of any minimal surface in the four dimensional Euclidean space satisfy an inequality, which generates two classes of minimal surfaces: minimal surfaces of general…
A ccc-generically supercompact cardinal $\kappa$ can be smaller than or equal to the continuum. On the other hand, such a cardinal $\kappa$ still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-$\tau$ metric. We establish an averaging bound for the cardinality of a code with prescribed minimum distance, discuss…
We prove upper bounds for the spread, the Lindel\"of number and the weak Lindel\"of number of the $G_\delta$-topology on a topological space and apply a few of our bounds to give a short proof to a recent result of Juh\'asz and van Mill…
The paper is an extensive and systematic study of cardinal invariants we call slalom numbers, describing the combinatorics of sequences of sets of natural numbers. Our general approach, based on relational systems, covers many such cardinal…
One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65--110, 1995], also known as the weak structure theorem, revealed the local structure of graphs…
We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of accessible functors. In the process, we show that these…