Related papers: Simple structures axiomatized by almost sure theor…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study…

We establish an approximate zero-one law for sentences of continuous logic over finite metric spaces of diameter at most $1$. More precisely, we axiomatize a complete metric theory $T_{\mathrm{as}}$ such that, given any sentence $\sigma$ in…

Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…

We prove that every set $A\subset\mathbb{Z}/p\mathbb{Z}$ with $\mathbb{E}_x\min(1_A*1_A(x),t)\le(2+\delta)t\mathbb{E}_x 1_A(a)$ is very close to an arithmetic progression. Here $p$ stands for a large prime and $\delta,t$ are small real…

There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $\omega_1^{CK}+1$. Makkai produced a structure of Scott…

We show that a locally symmetric space of noncompact type and with finite volume is quasi-isometric to the euclidean cone over a finite simplicial complex. A detailed analysis of metric properties yields a proof of a conjecture of Siegel.

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…

An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $\psi$.…

We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving $\omega$-categoricity and Ehrenfeuchtness under these combinations are…

We define the structure constants of almost complex, almost symplectic and Riemannian structures on a local Lie group

The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity theorems were discovered where tameness replaces strong…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

We classify the ultrahomogeneous complete 3-edge-coloured graphs (3-graphs) with simple theory. This extends Lachlan's result (a corollary of the Effective Classification Theorem for stable structures) classifying the stable homogeneous…

We introduce the concept of a prenormed model of a particular kind of finitary single-sorted first-order theories, interpreted over a category with finite products. These are referred to as prealgebraic theories, for the fact that their…

In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in…

We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…

Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…

We introduce the concept of an almost prime number generalizing a prime number. It turns out that a composite almost prime number must be a Carmichael number, in case it exists. We prove several properties of almost prime numbers and…