Related papers: Coanalytic Ultrafilter Bases

We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech…

We prove that for any Borel probability measure $\mu$ on $\mathbb R^n$ there exists a set $X\subset \mathbb R^n$ of $n+1$ points such that any $n$-variate quadratic polynomial $P$ that is nonnegative on $X$ (i.e. $P(x)\geq 0$, for every $x…

We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point $q$, we focus our attention to a ball centered at $q$ whose radius is controlled by a second scale parameter. We discuss an absolute…

We give an explicit list of all p-groups G with a cyclic subgroup of index p^2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also proved that such a K-basis does not exist for…

In [5] (=Terao, H.: Multiderivations of Coxeter arrangements. Inventiones math., 148 (2002) 659--674), we constructed a basis for the contact-order filtration of the module of derivations on the orbit space of a finite real reflection group…

We extend the basic theory of the coniveau and strong coniveau filtrations to the $\ell$-adic setting. By adapting the examples of Benoist--Ottem to the $\ell$-adic context, we show that the two filtrations differ over any algebraically…

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a…

Let q be a power of 2. We show by representation theory that there exists a q x q unitary matrix of multiplicative order q+1 whose powers generate q+1 pairwise mutually unbiased base in C^q. When q is a power of an odd prime, there is a q x…

In this paper we complete the attempt of H. Lefmann to show that Borel equivalence relations on the $n$-element subsets of $2^{\omega}$, that respect an order type, have a finite Ramsey basis.

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a…

It is well-known that the point cohomology of the convolution algebra $\ell^1({\mathbb Z}_+)$ vanishes in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point…

We study `definable' subsets of Baire space $\mathcal{N}$. The logic of our arguments is intuitionistic and we use L.E.J.~Brouwer's Thesis on bars in $\mathcal{N}$ and his continuity axioms. We avoid the operation of taking the complement…

A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a…

Let $X$ be an unbounded metric space, $B(x,r) = \{y\in X: d(x,y) \leqslant r\}$ for all $x\in X$ and $r\geqslant 0$. We endow $X$ with the discrete topology and identify the Stone-\v{C}ech compactification $\beta X$ of $X$ with the set of…

We give a partial answer to the following question of Dobrinen: For a given topological Ramsey space $\mathcal{R}$, are the notions of selective for $\mathcal{R}$ and Ramsey for $\mathcal{R}$ equivalent? Every topological Ramsey space…

For ultrafilters u,v on N, the operation u/v is introduced and formalised which acts as quotient-like structures when v strongly divides u.Central to our study is the characterization of self-divisible ultrafilters in connection with the…

We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and Pi11-Comprehension.

Let $\Phi$ be a finite crystallographic irreducible root system and $\mathcal P_{\Phi}$ be the convex hull of the roots in $\Phi$. We give a uniform explicit description of the polytope $\mathcal P_{\Phi}$, analyze the…

For a C$^{*}$-bialgebra $A$ with a comultiplication $\Delta$, a universal $R$-matrix of $(A,\Delta)$ is defined as a unitary element in the multiplier algebra $M(A\otimes A)$ of $A\otimes A$ which is an intertwiner between $\Delta$ and its…

We define a special version of the ultralimit, called the skewed ultralimit. Using this tool, we show that the set of ultrafilter types in the $C$-equivalence class of a Ramsey ultrafilter $\mathfrak u\in \beta\omega$ with the Rudin-Keisler…