arXiv math/93122041993-12-14math.LO

滤子的强弱性质

Strong meager properties for filters

Claude Laflamme

摘要：

分析了自然数上滤子在经典Baire性质和滤子为$F_σ$之间的几个"强弱“性质. Talagrand研究了两个这样的性质，并研究了几个组合性质。特别地，我们定义了P $^+$ -滤子的概念，它是传统P-滤子概念的推广，并证明了非贫乏P $^+$ -滤子的存在性.我们的动机在于理解的结构所产生的过滤器的补充的成员的一个极大几乎不相交的家庭。

英文摘要：

We analyze several ``strong meager'' properties for filters on the natural numbers between the classical Baire property and a filter being $F_σ$. Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P$^+$-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P$^+$-filter. Our motivation lies in understanding the structure of filters generated by complements of members of a maximal almost disjoint family.

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