Related papers: Admissible extensions of subtheories of second ord…

The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for admissible algebras with formal two-ray modules.

Given a field K, one may ask which finite groups are Galois groups of field extensions L/K such that L is a maximal subfield of a division algebra with center K. This connection between inverse Galois theory and division algebras was first…

We prove an inverse of Furstenberg's correspondence principle stating that for all measure preserving systems $(X,\mu,T)$ and $A\subset X$ measurable there exists a set $E \subset \mathbb{N}$ such that \[ \mu\left( \bigcap_{i=1}^k…

This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…

Let $\mathbb F$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of $\mathbb P^M(\mathbb F)$. In this paper, we will prove…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

The main results of this paper are the construction, both rigourous and intuitive, of "the" intrinsic extension of the set of non negative integers N and the smallest over-field of R set which is continue (according to R.Dedekind). The aim…

In this paper we construct a $(2,2)$ dimensional string theory with manifest $N=1$ spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The…

Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Menger's classic covering property. The methods…

We consider an almost o-minimal expansion of an ordered group $\mathcal M=(M,<,+,0,\ldots)$ and its tame extension $\mathcal N=(N,<,+,0,\ldots)$. We demonstrate that the subset $\{x \in M^n\;|\; \mathcal N \models \Phi(x,a)\}$ of $M^n$…

We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a…

The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…

A version of the second order phase transition theory, in which the Nernst theorem holds automatically, is proposed. The theory is constructed in terms of the order parameter and the (configurational) entropy. It faithfully reproduces the…

Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…

Topologies $\tau, \sigma$ on a set $X$ are called $\pi$-compatible if $\tau$ is a $\pi$-network for $\sigma$, and vice versa. If topologies $\tau, \sigma$ on a set $X$ are $\pi$-compatible then the families of nowhere dense sets (resp.…

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent…