Related papers: On the strong Freese-Nation property

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these…

Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results…

We observe almost divisibility for the original Cuntz semigroup of a simple AH algebra with strict comparison. As a consequence, the properties of strict comparison, finite nuclear dimension, and Z-stability are equivalent for such…

We study the holographic dual of a finite density system with both bosonic and fermionic degrees of freedom. There is no evidence for a universal bose-dominated ground state. Instead, depending on the relative conformal weights the…

We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this…

It was shown in Part I that there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski-dense. Here we show…

Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

Let $(X, +)$ denote $(\mathbb{R}, +)$ or $(2^{\omega}, +_2)$. We prove that for any meagre set $F \subseteq X$ there exists a subgroup $G \le X$ without the Baire property, disjoint with some translation of F. We point out several…

We introduce the weak Haagerup property for locally compact groups and prove several hereditary results for the class of groups with this approximation property. The class contains a priori all weakly amenable groups and groups with the…

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…

The framework of algebraically natural proofs was independently introduced in the works of Forbes, Shpilka and Volk (2018), and Grochow, Kumar, Saks and Saraf (2017), to study the efficacy of commonly used techniques for proving lower…

We give an elementary proof of a version of the implicit function theorem over Henselian valued fields $K$. It yields a density property for such fields (introduced in a joint paper with J. Koll{\'a}r), which is indispensable for ensuring…

Given a variety with a suitable Brauer class, we present a general pullback construction that produces varieties that has Brauer--Manin obstruction to the existence of rational points. We then study Severi--Brauer fibrations and their…

We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrodinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property called…

In this paper, we deal with soft MTL-algebras based on fuzzy sets. By means of $\in$-soft sets and q-soft sets, some characterizations of (Boolean, G- and MV-) filteristic soft MTL-algebras are investigated. Finally, we prove that a soft…

There has been recent debate over the use of the Boltzmann property in the kinetic equations describing dense neutrino systems such as early Universe and Supernova core. A technique developed by Bell, Rawlinson, and Sawyer utilises the…

The spectra of $N$-boson systems with arbitrary nonzero spin $\mathfrak{f}$ have been studied. Firstly, only the singlet pairing interaction is considered, a set of eigenstates together with the eigenenergies are analytically obtained. The…

Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…

We show that certain algebraic structures lack freeness in the absence of the axiom of choice. These include some subgroups of the Baer-Specker group $\mathbb{Z}^{\omega}$ and the Hawaiian earring group. Applications to slenderness,…