Related papers: A Universal Continuum of Weight aleph

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to…

We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+\alpha}$ diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary…

We prove that if less than $\aleph_{\omega}$-many Cohen reals are added to a model of \textsf{CH}, then $\omega^{\ast}$ can not be covered by nowhere dense \textsf{P}-sets (equivalently, there is an ultrafilter on $\omega$ that does not…

A set X which is a subset of the Cantor set has property (s) (Marczewski (Spzilrajn)) iff for every perfect set P there exists a perfect set Q contained in P such that Q is a subset of X or Q is disjoint from X. Suppose U is a nonprincipal…

In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real-valued functions on the Parovicenko space. This…

We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$-metric space to itself, the existence of a fixed point of $f$ is independent of the background model…

We state a new generic absoluteness principle, and use Shelah's memory iteration technique to show that it is consistent with the large continuum.

We prove that for $\mathcal{C}^{1,\alpha}$ diffeomorphisms on a compact manifold $M$ with ${\rm dim} M\leq 3$, if an invariant measure $\mu$ is a continuity point of the sum of positive Lyapunov exponents, then $\mu$ is an upper…

Let $M$ be a closed smooth manifold and let $f:M\to M$ be a diffeomorphism. $C^1$-generically, a continuum-wise expansive satisfies Axiom A without cycles. Moreover, there is a partially hyperbolic diffeomorphism $f$ such that it is not…

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital…

Assuming the continuum hypothesis there is an inseparable sequence of length omega_1 that contains no Lusin subsequence, while if Martin's Axiom and the negation of CH is assumed then every inseparable sequence (of length omega_1) is a…

Starting from the $\rm{GCH},$ we build a cardinal and $\rm{GCH}$ preserving generic extension of the universe, in which there exists a set $A \subseteq \omega_2$ of size $\aleph_2$ so that every countably infinite subset of $A$ or $\omega_2…

We prove that there exists a nonprincipal ultrafilter $\mathcal U$ on $\mathbb N$ such that for every countable (or separable) structure $B$ in a countable language the quotient map from the reduced product associated with the Fr\'echet…

We introduce and study the notion of entropy of affine permutations and prove that it coincides with the atomic length associated with the sum of the fundamental weights for a type $A$ affine root system, as defined by the first two…

In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…

In [FHK13], the authors considered the question whether model-existence of $L_{\omega_1,\omega}$-sentences is absolute for transitive models of ZFC, in the sense that if $V \subseteq W$ are transitive models of ZFC with the same ordinals,…

Let $0<p\leq 1$, $\omega$ be a weight on $\mathbb Z$, and let $\mathcal A$ be a unital Banach algebra. If $f$ is a continuous function from the unit circle $\mathbb T$ to $\mathcal A$ such that $\sum_{n\in \mathbb Z} \|\widehat f(n)\|^p…

We prove the consistency of ``CH + 2^{aleph_1} is arbitrarily large + 2^{aleph_1} not-> (omega_1 x omega)^2_2''. If fact, we can get 2^{aleph_1} not-> [omega_1 x omega]^2_{aleph_0}. In addition to this theorem, we give generalizations to…

The \emph{Filter Dichotomy} says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A function between topological…

We study some universal features of gravity in higher dimensions and by universal we mean a feature that remains true in all dimensions $\geq4$. They include: (a) the gravitational dynamics always follows from the Bianchi derivative of a…