English

Forcing Axioms, the Uniformization and the Basis Property

Logic 2025-06-17 v3

Abstract

We show that there are models of MA where the boldface Σ31\Sigma^1_3-uniformization property holds. Further we show that BPFA and the assertion 1\aleph_1 is accessible to reals outright implies that the boldface Σ31\Sigma^1_3-uniformization property is true.

Cite

@article{arxiv.2001.07977,
  title  = {Forcing Axioms, the Uniformization and the Basis Property},
  author = {Stefan Hoffelner},
  journal= {arXiv preprint arXiv:2001.07977},
  year   = {2025}
}

Comments

31 pages

R2 v1 2026-06-23T13:17:33.672Z