论文标题
Lightface $σ^1_2 $ - 可视化的红衣主教
Lightface $Σ^1_2$-indescribable cardinals
论文作者
论文摘要
$σ^1_3 $ -Absoluteness ccc强迫意味着对于任何CCC强迫$ p $，$ {H_ {ω_1}}}^V \ PROC_ {σ_2} {h_ {ω_1}}}}^{v^p} $。 “ $ω_1$无法访问真实”是指对于任何真正的$ r $，$ {ω_1}^{l [r]} <ω_1$。为了衡量“ $σ^1_3 $ -Absoluteness for CCC强迫和$ω_1$”的确切一致性强度无法访问Reals”，我们引入了一个弱紧凑的红衣主教的弱版本，即（Lightface）$σ^1_2^1_2 $ -IndeScrable-Indescrable Cardinal; $κ$如果无法访问，则完全具有此属性，并且$h_κ\ prec_ {σ_2} h_ {κ^+} $。
$Σ^1_3$-absoluteness for ccc forcing means that for any ccc forcing $P$, ${H_{ω_1}}^V \prec_{Σ_2}{H_{ω_1}}^{V^P}$. "$ω_1$ inaccessible to reals" means that for any real $r$, ${ω_1}^{L[r]}<ω_1$. To measure the exact consistency strength of "$Σ^1_3$-absoluteness for ccc forcing and $ω_1$ is inaccessible to reals", we introduce a weak version of a weakly compact cardinal, namely, a (lightface) $Σ^1_2$-indescribable cardinal; $κ$ has this property exactly if it is inaccessible and $H_κ\prec_{Σ_2} H_{κ^+}$.
