More on the Boolean Prime Ideal Theorem

Jacob Kowalczyk; Jindrich Zapletal

More on the Boolean Prime Ideal Theorem

Logic 2026-07-18 v1

Authors: Jacob Kowalczyk , Jindrich Zapletal

Abstract

We prove the consistency of Zermelo--Fraenkel set theory with the Axiom of Dependent Choices, no Vitali sets and a large fragment of the Boolean Prime Ideal Theorem.

Cite

@article{arxiv.2607.16747,
  title  = {More on the Boolean Prime Ideal Theorem},
  author = {Jacob Kowalczyk and Jindrich Zapletal},
  journal= {arXiv preprint arXiv:2607.16747},
  year   = {2026}
}