We show that Martin’s Maximum${}^{++}$ implies Woodin’s ${\mathbb P}_{\rm max}$ axiom $(*)$. This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are $\aleph _2$ many real numbers.

中文翻译：

---

Martin的Maximum $ {} ^ {++} $表示Woodin的公理$（*）$ | 数学年鉴

我们证明了马丁的Maximum $ {} ^ {++} $表示Woodin的$ {\ mathbb P} _ {\ rm max} $公理$（*）$。这回答了1990年代的一个问题，并将两个著名的集合论公理融合在一起，都已知这暗示着$ \ aleph _2 $包含许多实数。