English

Distinguishing Martin's axiom from its restrictions

Logic 2024-06-21 v1

Abstract

We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions satisfying the countable chain condition in all finite powers. Our method shows also the finer distinction, that Martin's axiom is strictly stronger than its restriction to forcing notions whose squares satisfy the countable chain condition.

Keywords

Cite

@article{arxiv.2406.13108,
  title  = {Distinguishing Martin's axiom from its restrictions},
  author = {Yinhe Peng},
  journal= {arXiv preprint arXiv:2406.13108},
  year   = {2024}
}