论文标题
弱扩展的红衣主教和延长逻辑的紧凑性
Weakly extendible cardinals and compactness of extended logics
论文作者
论文摘要
我们介绍了弱扩展的红衣主教的概念，并表明这些主要的枢机主教的特征是二阶逻辑的紧凑性弱。弱扩展的红衣主教的一致性强度和宽敞的性质位于强烈展开的（即精明的）红衣主教之间，并强烈提升了红衣主教。许多其他逻辑的紧凑性弱可以连接到弱扩展的红衣主教概念的某些变体。我们还表明，在V = L下，红衣主教$κ$是$ {\ cal l}^{\ aleph_0，ii} _ {stat，κ，ω} $的紧凑型弱，仅当它是薄弱的紧凑型$ {\ cal l}^^^{II} _} $的弱弱点。后一种条件等于条件是$κ$通过上述表征弱扩展（该等效性在没有V = l的情况下保持不变）。
We introduce the notion of weakly extendible cardinals and show that these cardinals are characterized in terms of weak compactness of second order logic. The consistency strength and largeness of weakly extendible cardinals are located strictly between that of strongly unfoldable (i.e. shrewd) cardinals, and strongly uplifting cardinals. Weak compactness of many other logics can be connected to certain variants of the notion of weakly extendible cardinals. We also show that, under V=L, a cardinal $κ$ is the weak compactness number of ${\cal L}^{\aleph_0,II}_{stat,κ,ω}$ if and only if it is the weak compactness number of ${\cal L}^{II}_{κ,ω}$. The latter condition is equivalent to the condition that $κ$ is weakly extendible by the characterization mentioned above (this equivalence holds without the assumption of V=L).
