Stranger Things about Forcing without AC
Martin Goldstern, Lukas Daniel Klausner
TL;DR
This paper explores how certain properties of forcing posets fail in ZF set theory without the Axiom of Choice, providing insights into the limitations of forcing in the absence of AC.
Contribution
It demonstrates that key properties of forcing posets do not hold without the Axiom of Choice, answering a question posed by Miller.
Findings
Several properties of forcing posets fail without AC
Answers Miller's question from arXiv:0704.3998
Highlights limitations of forcing in ZF set theory
Abstract
Typically, set theorists reason about forcing constructions in the context of ZFC. We show that without AC, several simple properties of forcing posets fail to hold, one of which answers Miller's question from arXiv:0704.3998.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.