منابع مشابه
Mad Families and Sane Player Sh935
We throw some light on the question: is there a MAD family (= a maximal family of infinite subsets of N, the intersection of any two is finite) which is saturated (= completely separable i.e. any X ⊆ N is included in a finite union of members of the family or includes a member (and even continuum many members) of the family). We prove that it is hard to prove the consistency of the negation: (a...
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Let κ < λ be regular uncountable cardinals. Using a finite support iteration of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.
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The notion of very mad family is a strengthening of the notion of mad family of functions. Here we show existence of very mad families in different contexts.
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We study several sorts of maximal almost disjoint families, both on a countable set and on uncountable, regular cardinals. We relate the associated cardinal invariants with bounding and dominating numbers and also with the uniformity of the meager ideal and some of its generalizations. 1. Who Are These Families? A Background Check Almost disjoint (ad) families have been a topic of interest in s...
متن کاملMAD families and the rationals
Rational numbers are used to classify maximal almost disjoint (MAD) families of subsets of the integers. Combinatorial characterization of indestructibility of MAD families by the likes of Cohen, Miller and Sacks forcings are presented. Using these it is shown that Sacks indestructible MAD family exists in ZFC and that b = c implies that there is a Cohen indestructible MAD family. It follows th...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2011
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-057-1