THE ORDERING PRINCIPLE AND DEPENDENT CHOICE
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 $\operatorname {\mathrm {ZF}}$ with the ordering principle together with a failure of the axiom of choice.
Authors
- Jonathan Schilhan (ORCID: https://orcid.org/0000-0001-6696-1603)
- Peter Holy (ORCID: https://orcid.org/0000-0001-8643-1845)
Institutions
- University of Vienna (AT)
Publication Details
- Journal
- Bulletin of Symbolic Logic
- Published
- 2025-11-03
- DOI
- https://doi.org/10.1017/bsl.2025.10130
- Primary Topic
- Advanced Algebra and Logic
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- UK Research and Innovation
- Austrian Science Fund
- Universität Wien
- Technische Universität Wien