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Consistency of strictly impredicative NF and a little more …

  • Sergei Tupailo (a1)
Abstract
Abstract

An instance of Stratified Comprehension

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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[7] R. B. Jensen , On the consistency of a slight(?) modification of Quine's NF, Synthese, vol. 19 (1969), pp. 250263.

[9] W. V. Quine , New Foundations for Mathematical Logic, The American Mathematical Monthly, vol. 44 (1937), pp. 7080.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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