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