Related papers: Borel Complexity and the Schr\"oder-Bernstein Prop…

We present a bound for the weak Lindel\"of number of the $G_\delta$-modification of a Hausdorff space which implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in…

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…

We show that, for every minimal action of a countably infinite discrete group on a compact metrizable space, if the extreme boundary of the simplex of invariant Borel probability measures is closed and has finite covering dimension then the…

We extend the quantum-mechanical results of Muller & Saunders (2008) establishing the weak discernibility of an arbitrary number of similar fermions in finite-dimensional Hilbert-spaces in two ways: (a) from fermions to bosons for all…

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable…

It has long been demonstrated that the vacuum scalar-tensor theory in the Jordan-frame Brans-Dicke parametrization is form-invariant under conformal transformations, provided that a suitable transformation of the coupling parameter $\omega$…

The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…

Let $X$ be a Polish space and $K$ a separable compact subset of the first Baire class on $X$. For every sequence $\bs$ dense in $\kk$, the descriptive set-theoretic properties of the set \[ \lbf=\{L\in[\nn]: (f_n)_{n\in L} \text{is…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…

Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval [0,1] is compact. In this article, we present a proof of this result that doesn't involve the standard techniques such as constructing a…

We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as the fundamental object of study. The connection…

We give a criterion for the weak convergence of unit Borel measures on the N-dimensional Berkovich projective space over a complete non-archimedean field. As an application, we give a sufficient condition for equidistribution in terms of a…

In this note we extend a recent result of S. Brendle [3] to Riemannian manifolds with densities and nonnegative Bakry-\'Emery Ricci curvature.

This article is the continuation of the first named author work "On maximal totally real embeddings". For real analytic compact manifolds equipped with a covariant derivative operator acting on the real analytic sections of its tangent…

For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$…

The (Local) Lifting Property ((L)LP) is introduced by Kirchberg and deals with lifting completely positive maps. We give a characterization of the (L)LP in terms of lifting $\ast$-homomorphisms. We use it to prove that if $A$ and $B$ have…

$\mathop{\rm rp}\nolimits ({\mathbb B})$ denotes the reduced power ${\mathbb B}^\omega /\Phi$ of a Boolean algebra ${\mathbb B}$, where $\Phi$ is the Fr\'{e}chet filter $\Phi$ on $\omega$. We investigate iterated reduced powers…

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…