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2012 On Existence in Set Theory
Rodrigo A. Freire
Notre Dame J. Formal Logic 53(4): 525-547 (2012). DOI: 10.1215/00294527-1722737


The aim of the present paper is to provide a robust classification of valid sentences in set theory by means of existence and related notions and, in this way, to capture similarities and dissimilarities among the axioms of set theory. In order to achieve this, precise definitions for the notions of productive and nonproductive assertions, constructive and nonconstructive productive assertions, and conditional and unconditional productive assertions, among others, will be presented. These definitions constitute the result of a semantical analysis of the notions involved. The conceptual clarification developed here results in a classification of valid sentences of set theory that goes against the standard view that extensionality is not an existence assertion.


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Rodrigo A. Freire. "On Existence in Set Theory." Notre Dame J. Formal Logic 53 (4) 525 - 547, 2012.


Published: 2012
First available in Project Euclid: 8 November 2012

zbMATH: 1266.03054
MathSciNet: MR2995418
Digital Object Identifier: 10.1215/00294527-1722737

Primary: 03E30

Rights: Copyright © 2012 University of Notre Dame


Vol.53 • No. 4 • 2012
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