Ideal independence, free sequences, and the ultrafilter number

Commentationes mathematicae Universitatis Carolinae

Kevin Selker¹ 

关键词: free sequences;    Boolean algebras;    cardinal functions;    ultrafilter number;   

DOI  :  10.14712/1213-7243.015.110

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komj\'ath P., {\it Boolean algebras in which every chain and antichain is countable\/}, Fund. Math. {\bf 111} (1981), 125--133, Koszmider P., {\it Forcing minimal extensions of Boolean algebras\/}, Trans. Amer. Math. Soc. {\bf 351} (1999), no.~8, 3073--3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, $A$ such that $\mathfrak{f}(A) = \text{s}_{\text{mm}}(A)

【 授权许可】

CC BY