超紧性的组合本质

摘要：

我们引入组合原理，刻画强紧性和超紧性的不可达基数，但也有意义的继任者的基数。它们的一致性是根据假定的最优值建立的。利用失败的一个弱版本的平方，我们表明，目前已知的最好的下界的一致性强度，这些原则可以应用。

英文摘要：

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.

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