论文标题
单一广义描述集理论的类似Solovay的模型
A Solovay-like model for singular generalized descriptive set theory
论文作者
论文摘要
库嫩证明了莱因哈特红衣主教的不存在证明，开辟了对大型红衣主教的研究，即以不一致的限制的假设。这些大型红衣主教之一I0被证明具有描述性理论特征，类似于确定性的公理所暗示的特征：如果$λ$证人I0 I0，则有$ v_ {λ+1} $的拓扑结构，它是完全可分离的，并且具有$λ$。 $ v_ {λ+1} $ in $ l（v_ {λ+1}）$具有$λ$ - 完美的设置属性。在本文中，我们发现了另一个奇异重量$κ$ cofinality $ω$的普遍的波兰空间，因此其所有子集都具有$κ$ - 完美的设置属性，并且在此过程中，我们将此类属性的一致性从I0降低至$κ$ $ $ $ $ $θ$ -supercpact，并带有$θ>κ$ ch $κ$ inaccessible。
Kunen's proof of the non-existence of Reinhardt cardinals opened up the research on very large cardinals, i.e., hypotheses at the limit of inconsistency. One of these large cardinals, I0, proved to have descriptive-set-theoretical characteristics, similar to those implied by the Axiom of Determinacy: if $λ$ witnesses I0, then there is a topology for $V_{λ+1}$ that is completely metrizable and with weight $λ$ (i.e., it is a $λ$-Polish space), and it turns out that all the subsets of $V_{λ+1}$ in $L(V_{λ+1})$ have the $λ$-Perfect Set Property in such topology. In this paper, we find another generalized Polish space of singular weight $κ$ of cofinality $ω$ such that all its subsets have the $κ$-Perfect Set Property, and in doing this, we are lowering the consistency strength of such property from I0 to $κ$ $θ$-supercompact, with $θ>κ$ inaccessible.
