English

The Ordering Principle and Dependent Choice

Logic 2026-01-14 v2

Abstract

We introduce finite support iterations of symmetric systems, and use them to provide a strongly modernized proof of David Pincus' classical result that the axiom of dependent choice is independent over ZF with the ordering principle together with a failure of the axiom of choice.

Keywords

Cite

@article{arxiv.2504.02744,
  title  = {The Ordering Principle and Dependent Choice},
  author = {Peter Holy and Jonathan Schilhan},
  journal= {arXiv preprint arXiv:2504.02744},
  year   = {2026}
}

Comments

17 pages

R2 v1 2026-06-28T22:45:33.779Z