论文标题
描述性集理论的新拓扑概括
A new topological generalization of descriptive set theory
论文作者
论文摘要
我们介绍了$σ$ -Projective层次结构的新拓扑概括，不仅限于波兰空间。较早的尝试已将$^ω$替换为$^κκ$，以$κ$常规的不可容纳，或者可计数$σ$ -Discrete代替。取而代之的是，我们在连续图像和完美的预映率下与可数的工会一起关闭了通常的$σ$ -proigntive集。自然设定的理论公理为$σ$ - 标志性的决定性，这是从大型红衣主教开始的。我们的目标是将已知的结果概括为$ k $分析空间（$^ωΩ$的完美预图像的连续图像），以将其概括为这些更一般的设置。我们在选择原则领域取得了一些成功 - 一般的主题是，定义的Menger Spaces是Hurewicz，甚至是$σ$ -Compact。 ZFC中的$ K $分析结果是正确的；更一般的结果具有仅无法访问的一致性强度。
We introduce a new topological generalization of the $σ$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^ωω$ by $^κκ$, for $κ$ regular uncountable, or replaced countable by $σ$-discrete. Instead we close the usual $σ$-projective sets under continuous images and perfect preimages together with countable unions. The natural set-theoretic axiom to apply is $σ$-projective determinacy, which follows from large cardinals. Our goal is to generalize the known results for $K$-analytic spaces (continuous images of perfect preimages of $^ωω$) to these more general settings. We have achieved some successes in the area of Selection Principles--the general theme is that nicely defined Menger spaces are Hurewicz or even $σ$-compact. The $K$-analytic results are true in ZFC; the more general results have consistency strength of only an inaccessible.
