${\sf MM}^{++}$ implies $(*)$
- Resource Type
- Working Paper
- Authors
- Asperó, David; Schindler, Ralf
- Source
- Subject
- Mathematics - Logic
- Language
We show that Martin's Maximum${}^{++}$ implies Woodin's ${\mathbb P}_{\rm max}$ 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 $\aleph_2$ many real numbers.
Comment: 48 pages. To appear in Annals of Mathematics