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December 2010 Consistency of strictly impredicative NF and a little more …
Sergei Tupailo
J. Symbolic Logic 75(4): 1326-1338 (December 2010). DOI: 10.2178/jsl/1286198149

Abstract

An instance of Stratified Comprehension

∀ x1…∀ xn∃ y∀ x (x∈ y ↔ φ(x,x1,…,xn))

is called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay.

As a bonus, our interpretation also satisfies some instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers.

Apparently, this is a new subsystem of NF shown to be consistent. The consistency question for the whole theory NF remains open (since 1937).

Citation

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Sergei Tupailo. "Consistency of strictly impredicative NF and a little more …." J. Symbolic Logic 75 (4) 1326 - 1338, December 2010. https://doi.org/10.2178/jsl/1286198149

Information

Published: December 2010
First available in Project Euclid: 4 October 2010

zbMATH: 1223.03034
MathSciNet: MR2767971
Digital Object Identifier: 10.2178/jsl/1286198149

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 4 • December 2010
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