Related papers: Extreme types and extremal models

The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…

We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…

Affine continuous logic is extended to affine integration logic. Affine compactness theorem is proved by both the ultramean construction and Henkin's method. Also, a proof system and a completeness theorem are given. An appropriate variant…

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal…

We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

We prove that the category of models of any relational Horn theory satisfying a mild syntactic condition is infinitely extensive. Central examples of such categories include the categories of preordered sets and partially ordered sets, and…

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of…

Let $K_{exp+}$ be the class of all structures $A$ such that the automorphism group of $A$ has at most $c n^{d n}$ orbits in its componentwise action on the set of $n$-tuples with pairwise distinct entries, for some constants $c,d$ with $d <…

We prove that the tensor product of a simple and a finite dimensional $\mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $\mathfrak{q}(n)$-supermodules to that of simple…

This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…