Van Douwen's diagram for dense sets of rationals
Van Douwen's diagram for dense sets of rationals
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DOI：
10.1016/j.apal.2005.07.003
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发表时间：
2006-11
期刊：
影响因子：
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通讯作者：
J. Brendle
中科院分区：
文献类型：
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作者：
J. Brendle
我们研究基数不变量的结构密集（Q）/nwd的密集集的有理数模无处密集集。证明了sQ≤min{s，add（M）}，从而对偶了已知的rQ≥max{r，cof（M）} [B.巴尔卡尔湾埃尔南德斯-埃尔南德斯湾Hrušák，Combinatorics of dense subsets of the rationals，Fund.Math.183（2004）59-80，Theorem 3.6].我们还证明了hQ<sQ和h<hQ的一致性。我们的结果回答了Balcar、Hernández和Hrušák的四个问题[B. Balcar，F. Hernán-Hernández，M. Hrušák，Combinatorics of dense subsets of the rationals，Fund. Math. 183（2004）59-80，Questions 3.11]。
We investigate cardinal invariants related to the structure Dense(Q)/nwd of dense sets of rationals modulo the nowhere dense sets. We prove that sQ≤min{s,add(M)}, thus dualizing the already known rQ≥max{r,cof(M)} [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 (2004) 59–80, Theorem 3.6]. We also show the consistency of each of hQ<sQand h<hQ. Our results answer four questions of Balcar, Hernández and Hrušák [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 (2004) 59–80, Questions 3.11].