Elementary approximation theory
type: Item
instance of: scholarly article
title: Elementary approximation theory
zbMATH Open document ID: 0762.03015
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1993-01-16T00:00:00Z
review text: We consider elementary approximation theory [see \textit{H. Rasiowa} and \textit{A. Skowron}, Proc. Int. Spring Sch., Wendisch-Rietz/GDR 1985, Math. Res. 31, 123-139 (1986; Zbl 0642.68040)]. Our aim is to investigate some aspects concerning finite models of this theory. This motivates us to consider properties of finite models of a given first-order theory \(T\). Let \(\text{Th((Mod }T)_{\text{fin}})\) \((\text{Th}((\text{Mod }T)_{\inf})\), respectively) be the set of all sentences valid in the class of all finite (infinite, respectively) models of \(T\). The following natural questions arise: 1. What are the necessary and sufficient conditions for the equality \(T=\text{Th}((\text{Mod }T)_{\text{fin}})\)? 2. For which theories \(T\) is the theory \(\text{Th}((\text{Mod }T)_{\text{fin}})\) decidable? This paper is organized into three parts. In Section 1 we give some general facts concerning the first question. It also contains simple examples of finitely axiomatizable first-order theories \(T\) such that \(T=\text{Th}((\text{Mod }T)_{\text{fin}})\). In Section 2 we present some elementary approximation theories. It also contains results concerning questions 1 and 2 for these theories. In Section 3 we consider some approximation problems. In particular a notion of an approximating translation is formulated.
Mathematics Subject Classification ID: 03C13
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 92878
zbMATH Keywords: elementary approximation theory
zbMATH Keywords: finite models
zbMATH Keywords: finitely axiomatizable first-order theories
zbMATH Keywords: approximating translation
author: Jarosław Stepaniuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 92878