Related papers: A Borel maximal eventually different family
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $abc$ conjecture holds, generate distinct monogenic quartic fields infinitely often. Additional families (also…
We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard…
We study two different types of (maximal) almost disjoint families: very mad families and (maximal) cofinitary groups. For the very mad families we prove the basic existence results. We prove that MA implies there exist many pairwise…
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
We develop structure theory of finite Lie conformal superalgebras.
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
The first examples of exceptional terminal singularities are constructed.
We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…
We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.
We investigate and compare $\mathcal F$-Borel classes and absolute $\mathcal F$-Borel classes. We provide precise examples distinguishing these two hierarchies. We also show that for separable metrizable spaces, $\mathcal F$-Borel classes…
For Van Douwen families, maximal families of eventually different permutations and maximal ideal independent families we show that the existence of a $\Sigma^1_2$ family implies the existence of a $\Pi^1_1$ family of the same size. We also…
There exists a family $\{B_{\alpha}\}_{\alpha<\omega_1}$ of sets of countable ordinals such that o $\max B_{\alpha}=\alpha$, o if $\alpha\in B_{\beta}$ then $B_{\alpha}\subseteq B_{\beta}$, o if $\lambda\leq \alpha$ and $\lambda$ is a limit…
In order to better understand the structure of closed collections of reversible gates, we investigate the lattice of closed sets and the maximal members of this lattice. In this note, we find the maximal closed sets over a finite alphabet.…
We provide an infinite family of sofic one-relator groups that are not residually solvable nor residually finite. The proof is essentially different from the one in [1], as it does not require just Magnus' decompositions.
We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.