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We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classic results of Magidor (from 1977 and…

Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the L\"owenheim-Skolem Theorems of stationary logics. In this paper, we mainly analyze the…

Let $S=\{s_{n}\}$ be an increasing finite or infinite subset of $\mathbb N \bigcup \{0\}$ and $X(S)$ the $S$-gap shift associated to $S$. Let $f_{S}(x)=1-\sum\frac{1}{x^{s_{n}+1}}$ be the entropy function which will be vanished at…

An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that if A is norm-closed and strictly semi-transitive, then every…

The Noetherian type of a space X, Nt(X), is the least cardinal kappa such that X has a base B such that every element of the base is contained in less than kappa many elements of the base. Denote X the space obtained from 2^{aleph_omega} by…

On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…

We give necessary and sufficient conditions for a real-valued quasiconvex function f on a Baire topological vector space X (in particular, Banach or Frechet space) to be continuous at the points of a residual subset of X. These conditions…

Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar…

We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a…

Several important properties of positive semidefinite processes of Ornstein--Uhlenbeck type are analysed. It is shown that linear operators of the form $X\mapsto AX+XA^{\mathrm{T}}$ with $A\in M_d(\mathbb{R})$ are the only ones that can be…

Our "long term and large scale" aim is to characterize the first order theories T (at least the countable ones) such that: for every ordinal alpha there lambda,M_1,M_2 such that M_1,M_2 are non-isomorphic models of T of cardinality lambda…

A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is…

Let $f=(f^x\mid x\in S)$, $S\subset\mathbb{Z}^m$, be a semigroup of ergodic measure-preserving transformations of a probability space $(\Omega,\mathsf{P})$ and $h$ a real random function on $S$, such that $h(x+y,\omega)\le…

Let a finite non-empty X is equipped with discrete topology. We prove that S \subseteq X^\omega is of second category if and only if for each f:\omega -> \bigcup_{n \in \omega} X^n there exists a sequence {a_n}_{n \in \omega} belonging to S…

We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…

A shelf is a set with a binary operation~$\op$ satisfying $a \op (b \op c) = (a \op b) \op (a \op c)$. Racks are shelves with invertible translations $b \mapsto a \op b$; many of their aspects, including cohomological, are better understood…

In this paper we give characterizations of the super-stable theories, in terms of an external property called representation. In the sense of the representation property, the mentioned class of first-order theories can be regarded as "not…

We show that for 1<n<m, the class Nr_nCA_m known to be non-elementary is pseudo elementary. When n and m are finite we use a two sorted theory, when n is finite and m infinite we use a three sorted one, and finally when both are infinite we…

Let $M$ be a finite von Neumann algebra. In the first part, we give asymptotic results about $M$-stable sequences of weak*-continuous mappings which are related with operators belonging to $M$. In the second part, we extend, by a shorter…

F. Wehrung has asked: Given a family $\mathcal{C}$ of subsets of a set $\Omega$, under what conditions will there exist a total ordering on $\Omega$ under which every member of $\mathcal{C}$ is convex? <p> Note that if $A$ and $B$ are…