Translator Disclaimer
2017 Dunn–Priest Quotients of Many-Valued Structures
Thomas Macaulay Ferguson
Notre Dame J. Formal Logic 58(2): 221-239 (2017). DOI: 10.1215/00294527-3838853

Abstract

J. Michael Dunn’s Theorem in 3-Valued Model Theory and Graham Priest’s Collapsing Lemma provide the means of constructing first-order, three-valued structures from classical models while preserving some control over the theories of the ensuing models. The present article introduces a general construction that we call a Dunn–Priest quotient, providing a more general means of constructing models for arbitrary many-valued, first-order logical systems from models of any second system. This technique not only counts Dunn’s and Priest’s techniques as special cases, but also provides a generalized Collapsing Lemma for Priest’s more recent plurivalent semantics in general. We examine when and how much control may be exerted over the resulting theories in particular cases. Finally, we expand the utility of the construction by showing that taking Dunn–Priest quotients of a family of structures commutes with taking an ultraproduct of that family, increasing the versatility of the tool.

Citation

Download Citation

Thomas Macaulay Ferguson. "Dunn–Priest Quotients of Many-Valued Structures." Notre Dame J. Formal Logic 58 (2) 221 - 239, 2017. https://doi.org/10.1215/00294527-3838853

Information

Received: 25 April 2014; Accepted: 30 July 2014; Published: 2017
First available in Project Euclid: 21 February 2017

zbMATH: 06751300
MathSciNet: MR3634978
Digital Object Identifier: 10.1215/00294527-3838853

Subjects:
Primary: 03C90
Secondary: 03C20

Rights: Copyright © 2017 University of Notre Dame

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.58 • No. 2 • 2017
Back to Top