WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

被引：0

作者：

Hathaway, Dan ^{[1
]}

机构：

[1] Univ Denver, Dept Math, Denver, CO 80208 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2016年 / 81卷 / 02期

关键词：

Set Theory; complete Boolean algebras; distributive laws; weak distributivity; weakly compact cardinals; the tower number;

D O I：

10.1017/jsl.2015.63

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B be a complete Boolean algebra. We show that if lambda is an infinite cardinal and B is weakly (lambda(omega), omega)-distributive, then B is (lambda, 2)-distributive. Using a similar argument, we show that if kappa is a weakly compact cardinal such that B is weakly (2(kappa), kappa)-distributive and B is (alpha, 2)-distributive for each alpha < kappa, then B is (kappa, 2)-distributive.

引用

页码：711 / 717

页数：7

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