منابع مشابه
Projective wellorders and mad families with large continuum
We show that b = c = ω3 is consistent with the existence of a ∆3-definable wellorder of the reals and a Π2-definable ω-mad subfamily of [ω] ω (resp. ω).
متن کاملVery Mad Families
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.
متن کاملMad families, splitting families and large continuum
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.
متن کاملMad Families and Their Neighbors
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: Annals of Pure and Applied Logic
سال: 2010
ISSN: 0168-0072
DOI: 10.1016/j.apal.2010.06.007