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1.
In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $mathsf {CH}$ by adding a real. 相似文献
2.
Istvá n Juhá sz Peter Nyikos Zoltá n Szentmikló ssy 《Proceedings of the American Mathematical Society》2005,133(9):2741-2750
We give restrictions on the cardinality of compact Hausdorff homogeneous spaces that do not use other cardinal invariants, but rather covering and separation properties. In particular, we show that it is consistent that every hereditarily normal homogeneous compactum is of cardinality . We introduce property wD(), intermediate between the properties of being weakly -collectionwise Hausdorff and strongly -collectionwise Hausdorff, and show that if is a compact Hausdorff homogeneous space in which every subspace has property wD( ), then is countably tight and hence of cardinality . As a corollary, it is consistent that such a space is first countable and hence of cardinality . A number of related results are shown and open problems presented.