Consistency of strictly impredicative NF and a little more …

Journal of Symbolic Logic 75 (4):1326-1338 (2010)
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Abstract

An instance of Stratified Comprehension ∀x₁ … ∀x n ∃y∀x (x ∈ y ↔ φ(x, x₁, …, x n )) 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)

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Citations of this work

Alternative axiomatic set theories.M. Randall Holmes - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
[Omnibus Review].Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.

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