论文标题
Menger猜想的力量
The Strength of Menger's Conjecture
论文作者
论文摘要
Menger猜想R的R子集与Menger属性必须为$σ$ -COMPACT。虽然这是错误的，而对于R的子集没有限制，但对于投影子集而言，众所周知，它是从投影确定性的公理开始的，该确定性具有相当大的基本一致性强度。我们注意到，实际上，Menger对投影集的猜想仅具有无法接近的红衣主教的一致性强度。
Menger conjectured that subsets of R with the Menger property must be $σ$-compact. While this is false when there is no restriction on the subsets of R, for projective subsets it is known to follow from the Axiom of Projective Determinacy, which has considerable large cardinal consistency strength. We note that in fact, Menger's conjecture for projective sets has consistency strength of only an inaccessible cardinal.
