Extensionality and restriction in naive set theory
type: Item
instance of: scholarly article
title: Extensionality and restriction in naive set theory
zbMATH Open document ID: 1200.03021
author: Zach Weber
published in: Studia Logica
publication date: 2010-04-26T00:00:00Z
review text: The author discusses the possibility of having a nontrivial (but possibly inconsistent) naive set theory (i.e. one with comprehension and extensionality) within a paraconsistent relevant logic. He shows that one such set theory, proposed by \textit{J. Beall, R. T. Brady, A. P. Hazen, G. Priest} and \textit{G. Restall} [J. Philos. Log. 35, No. 6, 587--598 (2006; Zbl 1111.03020)], which uses a restricted arrow given by \(B\mapsto C := B \wedge t \rightarrow C\), for some theorem \(t\), and a subset relation \(a\subseteq b := \forall x( x \in a \mapsto x \in b)\) with the rule \(a\subseteq b \wedge b\subseteq a \vdash A(a) \mapsto A(b)\), is trivial.
reviewed by: Martin W. Bunder
Mathematics Subject Classification ID: 03B53
Mathematics Subject Classification ID: 03B47
Mathematics Subject Classification ID: 03E30
zbMATH DE Number: 5701668
zbMATH Keywords: naive set theory
zbMATH Keywords: relevant logic
zbMATH Keywords: paraconsistent logic
zbMATH Keywords: triviality
zbMATH Keywords: restricted quantification
MaRDI profile type: Publication
full work available at URL: s11225-010-9225-y
OpenAlex ID: W2066673753
cites work: Frontiers of paraconsistent logic. Papers from the 1st world congress on paraconsistency, Ghent, Belgium, July 30--August 2, 1997
cites work: Relevant restricted quantification
cites work: The Axiom of Comprehension in Infinite Valued Logic.
cites work: The inconsistency of certain formal logics
cites work: Relevant predication. I: The formal theory
cites work: Q3320365
cites work: Q3803101
cites work: Q4044481
cites work: Relevant identity
cites work: Models for a paraconsistent set theory
cites work: Semantics for relevance logic with identity
cites work: Q4198728
cites work: Logic without contraction as based on inclusion and unrestricted abstraction
cites work: Sense, entailment and modus ponens
cites work: Q3992933
cites work: Q3483259
cites work: Q4440565
cites work: Q3518425
cites work: Q3474639
cites work: Q4692665
cites work: Naïve comprehension and contracting implications
cites work: Q3874167
cites work: Q3470456
cites work: Q5573940
cites work: TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
cites work: The consistency of the axiom of comprehension in the infinite-valued predicate logic of Lukasiewicz
DOI: 10.1007/S11225-010-9225-Y
description: scientific article; zbMATH DE number 5701668