Related papers: An introduction to o-minimal structures
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small…
The main results on the theory of conformal and almost Grassmann structures are presented. The common properties of these structures and also the differences between them are outlined. In particular, the structure groups of these structures…
Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann…
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…
We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
Given a weakly o-minimal structure $\mathcal M$ and its o-minimal completion $\bar {\mathcal M}$, we first associate to $\bar {\mathcal M}$ a canonical language and then prove that $Th(\mathcal M)$ determines $Th(\bar {\mathcal M})$. We…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Some examples and basic properties of ultrametric spaces are briefly discussed.
In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact…
We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
The aim of this note is to determine whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of o-minimal structures and the real field with a discrete…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…