Related papers: Cardinal sequences of LCS spaces under GCH
Given a strong limit cardinal $\lambda$ of countable cofinality, we show that if every $\lambda$-coanalytic subset of the generalised Cantor space ${}^{\lambda}2$ has the $\lambda$-$\mathsf{PSP}$, then there is an inner model with…
Much recent work in cardinal characteristics has focused on generalizing results about $\omega$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$…
We answer a question of Krueger by obtaining -- from countably many Mahlo cardinals -- a model where there is a disjoint stationary sequence on $\aleph_{n+2}$ for every $n\in\omega$. In that same model, the notions of being internally…
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the…
Using the natural extension of the notion of the generalized coherent states the scalar and spinor ones for the de Sitter group SO(4,1) are constructed. These systems of coherent states obey the de Sitter--invariant Klein-Gordon and Dirac…
In this paper we continue to study of properties of $S(n)$-spaces. We establish bounded on the cardinality of $S(n)$-spaces.
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
We study minimally Terracini finite sets of points in the projective plane and we prove that the sequence of the cardinalities of minimally Terracini sets can have any number of gaps for degree great enough.
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved.…
We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…
The Generalized Locally Toeplitz (GLT) sequences of matrices have been originated from the study of certain partial differential equations. To be more precise, such matrix sequences arise when we numerically approximate some partial…
It is proved that every second countable locally Hausdorff and locally compact continuous groupoid has a Borel set of units that meets every orbit and is what is called "lacunary," a property that implies that the intersection with every…
We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn.
We introduce an extended setting to study Hecke pairs $(G,H)$ which admit a regular representation on $L^2(H\backslash G)$, and consequently a $C^*$-algebra. As the result, many pairs of locally compact groups which had been studied in…
In this note we introduce several instructive examples of bijections found between several different combinatorially defined sequences of sets. Each sequence has cardinalities given by the Catalan numbers. Our results answer some questions…
Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is \chi-tame. If K is categorical in some \lambda^+ >LS(K) then it is categorical…
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the…
We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…
We characterize noncommutative symmetric Banach spaces for which every bounded sequence admits either a convergent subsequence, or a $2$-co-lacunary subsequence. This extends the classical characterization, due to R\"abiger.
We present the formalization of Specker's "local" version of the claim that the Generalized Continuum Hypothesis implies the Axiom of Choice, with particular attention to some extra complications which were glossed over in the original…