English

NF is Consistent

Logic 2025-06-23 v23

Abstract

In this paper we will present a proof of the consistency of Quine's set theory "New Foundations" (hereinafter NF), so-called after the title of the 1937 paper in which it was introduced. This version takes the approach of building a model of tangled type theory rather than a model of the usual set theory without choice with a tangled web of cardinals; further, details of the construction are refined due to interaction with the now complete verification in Lean by the second author.

Keywords

Cite

@article{arxiv.1503.01406,
  title  = {NF is Consistent},
  author = {M. Randall Holmes and Sky Wilshaw},
  journal= {arXiv preprint arXiv:1503.01406},
  year   = {2025}
}

Comments

The latest version of these documents is always visible on my home page http://randall-holmes.github.io and it will be updated there more often then here

R2 v1 2026-06-22T08:44:29.859Z