English

${\sf MM}^{++}$ implies $(*)$

Logic 2021-03-19 v2

Abstract

We show that Martin's Maximum++{}^{++} implies Woodin's Pmax{\mathbb P}_{\rm max} axiom ()(*). This answers a question from the 1990's and amalgamates two prominent axioms of set theory which were both known to imply that there are 2\aleph_2 many real numbers.

Cite

@article{arxiv.1906.10213,
  title  = {${\sf MM}^{++}$ implies $(*)$},
  author = {David Asperó and Ralf Schindler},
  journal= {arXiv preprint arXiv:1906.10213},
  year   = {2021}
}

Comments

48 pages. To appear in Annals of Mathematics

R2 v1 2026-06-23T10:02:26.308Z