Representation and preservation of the metamathematical quotients of A. Robinson
type: Item
instance of: scholarly article
title: Representation and preservation of the metamathematical quotients of A. Robinson
zbMATH Open document ID: 0782.03015
DOI: 10.1007/BF01196102
published in: Algebra Universalis
publication date: 1993-07-18T00:00:00Z
review text: The concept of metamathematical ideal in structures, developed by A. Robinson, generalizes the notion of (algebraic) congruence in two ways: it takes into account the predicates of the language, and also it is defined relatively to a given theory. A concept of quotient follows. This paper solves the problem of characterizing the theories preserving these quotients, raised by \textit{A. F. Margarit} and \textit{L. M. Laita} [Z. Math. Logik Grundlagen Math. 33, 497-505 (1987; Zbl 0639.03036)]. It is found that such theories are those equivalent to a union of Positive and of Universal Strict Horn sentences (by showing first that the class \(Q(T^*)\) of the quotients of all models of \(T\) is \(H(T^*)\cap\text{SP}(T^*)\)).
Mathematics Subject Classification ID: 03C40
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 08C10
zbMATH DE Number: 203159
zbMATH Keywords: metamathematical quotients
zbMATH Keywords: preservation theorem
zbMATH Keywords: syntactic characterization
zbMATH Keywords: metamathematical ideal
zbMATH Keywords: Horn sentences
author: Michel Hébert
reviewed by: Michel Hébert
MaRDI profile type: Publication
cites work: Q3934450
cites work: Preservation and Interpolation Through Binary Relations Between Theories
full work available at URL: https://doi.org/10.1007/bf01196102
OpenAlex ID: W2072122061
Recommended article: Abraham Robinson's Meta-Algebra Revisited
Recommended article: A Framework for Metamathematics
Recommended article: Applied model theory and metamathematics. An Abraham Robinson memorial problem list
Recommended article: A representation theorem for quantales
Recommended article: On the metamathematics of algebra
Recommended article: Q4885261
Recommended article: Representation Theorems for Quantales
Recommended article: Q4346400
description: scientific article; zbMATH DE number 203159