SELECTIVELY (a)-SPACES FROM ALMOST DISJOINT FAMILIES ARE NECESSARILY COUNTABLE UNDER A CERTAIN PARAMETRIZED WEAK DIAMOND PRINCIPLE

被引：0

作者：

Morgan, Charles J. G. ^{[1
,2
]}

da Silva, Samuel G. ^{[3
]}

机构：

[1] UCL, Dept Math, Gower St, London WC1E 6BT, England

[2] Univ Lisbon, Ctr Matemat & Aplicacoes Fundamentais, Ave Prof Gama Pinto 2, P-1649003 Lisbon, Portugal

[3] Univ Fed Bahia, Inst Matemat, Campus Ondina,Ave Adhemar Barros S-N, BR-40170110 Salvador, BA, Brazil

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2016年 / 42卷 / 03期

关键词：

Almost disjoint families; star covering properties; property (a); selection principles; selectively (a); parametrized weak diamond principles;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The second author has recently shown ([20]) that any selectively (a) almost disjoint family must have cardinality strictly less than so under the Continuum Hypothesis such a family is necessarily countable. However, it is also shown in the same paper that 2(aleph 0) < 2(aleph 1) alone does not avoid the existence of uncountable selectively (a) almost disjoint families. We show in this paper that a certain effective parametrized weak diamond principle is enough to ensure countability of the almost disjoint family in this context. We also discuss the deductive strength of this specific weak diamond principle (which is consistent with the negation of the Continuum Hypothesis, apart from other features).

引用

页码：1031 / 1046

页数：16