Thin stationary sets and disjoint club sequences期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Thin stationary sets and disjoint club sequences

Authors:	Sy-David Friedman John Krueger

Institution:	Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Waehringer Strasse 25, A-1090 Wien, Austria ; Department of Mathematics, University of California, Berkeley, California 94720

Abstract:	We describe two opposing combinatorial properties related to adding clubs to $\omega_2$ : the existence of a thin stationary subset of $P_{\omega_1}(\omega_2)$ and the existence of a disjoint club sequence on $\omega_2$ . A special Aronszajn tree on $\omega_2$ implies there exists a thin stationary set. If there exists a disjoint club sequence, then there is no thin stationary set, and moreover there is a fat stationary subset of $\omega_2$ which cannot acquire a club subset by any forcing poset which preserves $\omega_1$ and $\omega_2$ . We prove that the existence of a disjoint club sequence follows from Martin's Maximum and is equiconsistent with a Mahlo cardinal.

Keywords:

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文