Related papers: A Borel maximal eventually different family
For a cardinal lambda<lambda_{omega_1} we give a ccc forcing notion P which forces that for some Borel subset B of the Cantor space (1) there a sequence (eta_alpha:alpha<lambda) of distinct elements such that |(eta_alpha+B) cap…
Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring. We concentrate on the minimal Hilbert series, which is…
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, at a certain point $c,$ depending on the chosen family $\{F_i \}$. The most important example is a polynomial with $c=1.$…
We constructed a parametrized family of Mordell curves with the rank of at least three.
We prove that the category of generalized holomorphically contractible families possesses maximal and minimal objects. Moreover, we present basic properties of these extremal families.
We review the results having the property of maximal transcendentality.
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…
We construct a family of infinite degree tt-rings, giving a negative answer to an open question by P. Balmer.
We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.
We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.
We construct a new family of N-fold supersymmetric systems which is referred to as ``type B''. A higher derivative representation of the N-fold supercharge for this new family is given by a deformation of the type A N-fold supercharge. By…
In this paper, we construct six families of infinite simple conformal superalgebra of finite growth based on our earlier work on constructing vertex operator superalgebras from graded assocaitive algebras. Three subfamilies of these…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
An infinite family of nonschurian separable association schemes is constructed.
Using countable support iteration of $S$-proper posets, for some appropriate stationary set $S$, we obtain a generic extension of the constructible universe, in which $\mathfrak{b}=\mathfrak{c}=\aleph_2$ and there is a maximal cofinitary…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
We consider two families of planar self-similar tilings of different nature: the tilings consisting of translated copies of the fractal sets defined by an iterated function system, and the tilings obtained as a geometrical realization of a…
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…
We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.