Related papers: On Erdos--Dushnik--Miller theorem without AC

We demonstrate a set A and a value of s for which the sequence of N-point discrete minimal Riesz s-energy configurations on A does not have an asymptotic distribution in the weak-star sense as N tends to infinity.

In this paper it is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal points; and the other one is proximal. Also for independent…

In this paper, we describe the formalization of the axiom of choice and several of its famous equivalent theorems in Morse-Kelley set theory. These theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal principle,…

For a countable, weakly minimal theory, we show that the Schroeder-Bernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to both a condition on orbits of rank 1 types and the property that the theory…

This note establishes a new weak mean ergodic theorem for 1-cocycles associated to weakly mixing representations of amenable groups.

We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.

In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing…

We introduce finite support iterations of symmetric systems, and use them to provide a strongly modernized proof of David Pincus' classical result that the axiom of dependent choice is independent over ZF with the ordering principle…

A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…

In arXiv:1811.04649, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras to the entire category weak modules and applied this result to Whittaker modules. In this paper we present further…

We establish the well-posedness of linear elliptic equations with critical-order drifts in $L^d$ and positive zero-order coefficients in $L^1$ or $L^{\frac{2d}{d+2}}$, where classical methods are often too restrictive. Our approach relies…

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…

We construct weak (i.e. non-graded) modules over the vertex operator algebra $M(1)^+$, which is the fixed-point subalgebra of the higher rank free bosonic (Heisenberg) vertex operator algebra with respect to the $-1$ automorphism. These…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…

We consider uniformly (DC) or periodically (AC) driven generalized infinite elastic chains (a generalized Frenkel-Kontorova model) with gradient dynamics. We first show that the union of supports of all the invariant measures, denoted by A,…

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…

Fix a vector space over a finite field and a system of linear equations. We provide estimates, in terms of the dimension of the vector space, of the maximum of the sizes of subsets of the space that do not admit solutions of the system…

Higher order set theory has been a topic of interest for some time, with recent efforts focused on the strength of second order set theories [KW16]. In this paper we strive to present one 'theory of collections' that allows for a formal…