论文标题
一般可扩展的红衣主教
Generically extendible cardinals
论文作者
论文摘要
在本文中，我们研究了一般可扩展的红衣主教的概念，这是可扩展的红衣主教的通用版本。我们证明，$ω_1$或$ω_2$的通用扩展性具有较小的一致性强度，但是红衣主教$>ω_2$的一致性没有。我们还考虑了一些与一般可扩展的红衣主教有关的结果，例如坚不可摧，真实的一般绝对性以及布尔值有价值的二阶逻辑。
In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $ω_1$ or $ω_2$ has small consistency strength, but that of a cardinal $>ω_2$ does not. We also consider some results concerned with generically extendible cardinals, such as indestructibility, generic absoluteness of the reals, and Boolean valued second order logic.
