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2014 Beneš’s Partial Model of NF: An Old Result Revisited
Edoardo Rivello
Notre Dame J. Formal Logic 55(3): 397-411 (2014). DOI: 10.1215/00294527-2688087


A paper by Beneš, published in 1954, was an attempt to prove the consistency of NF (Quine’s set theory “New Foundations”) via a partial model of Hailperin’s finite axiomatization of NF. Here, I offer an analysis of Beneš’s proof in a De Giorgi-style setting for set theory. This approach leads to an abstract version of Beneš’s theorem that emphasizes the monotone and invariant content of the axioms proved to be consistent, in a sense of monotony and invariance that this paper intends to state rigorously and to help clarify. Moreover, some tentative speculation will be made about possible developments of the topic in the following two directions: (1) which set theories can be proved to be consistent via Beneš-like constructions, and (2) how can we elaborate on Beneš’s model to get a consistency proof for full NF?


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Edoardo Rivello. "Beneš’s Partial Model of NF: An Old Result Revisited." Notre Dame J. Formal Logic 55 (3) 397 - 411, 2014.


Published: 2014
First available in Project Euclid: 22 July 2014

zbMATH: 1337.03078
MathSciNet: MR3263535
Digital Object Identifier: 10.1215/00294527-2688087

Primary: 03E70
Secondary: 03C30 , 03C62

Keywords: comprehension , New foundations , Set theory

Rights: Copyright © 2014 University of Notre Dame

Vol.55 • No. 3 • 2014
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