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2014 The Axiom Scheme of Acyclic Comprehension
Zuhair Al-Johar, M. Randall Holmes, Nathan Bowler
Notre Dame J. Formal Logic 55(1): 11-24 (2014). DOI: 10.1215/00294527-2377851

Abstract

A “new” criterion for set existence is presented, namely, that a set {x|ϕ} should exist if the multigraph whose nodes are variables in ϕ and whose edges are occurrences of atomic formulas in ϕ is acyclic. Formulas with acyclic graphs are stratified in the sense of New Foundations, so consistency of the set theory with weak extensionality and acyclic comprehension follows from the consistency of Jensen’s system NFU. It is much less obvious, but turns out to be the case, that this theory is equivalent to NFU: it appears at first blush that it ought to be weaker. This paper verifies that acyclic comprehension and stratified comprehension are equivalent by verifying that each axiom in a finite axiomatization of stratified comprehension follows from acyclic comprehension.

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Zuhair Al-Johar. M. Randall Holmes. Nathan Bowler. "The Axiom Scheme of Acyclic Comprehension." Notre Dame J. Formal Logic 55 (1) 11 - 24, 2014. https://doi.org/10.1215/00294527-2377851

Information

Published: 2014
First available in Project Euclid: 20 January 2014

zbMATH: 1327.03041
MathSciNet: MR3161409
Digital Object Identifier: 10.1215/00294527-2377851

Subjects:
Primary: 03E70

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 1 • 2014
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