Perfectly meager sets and universally null sets
نویسندگان
چکیده
منابع مشابه
Universally Meager Sets
We study category counterparts of the notion of a universal measure zero set of reals. We say that a set A ⊆ R is universally meager if every Borel isomorphic image of A is meager in R. We give various equivalent definitions emphasizing analogies with the universally null sets of reals. In particular, two problems emerging from an earlier work of Grzegorek are
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A set X ⊆ R is strongly meager if for every measure zero set H, X + H = R. Let SM denote the collection of strongly meager sets. We show that assuming CH, SM is not an ideal.
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We prove several equivalences and relative consistency results involving notions of generic absoluteness beyond Woodin’s (Σ ̃ 1)λ generic absoluteness for a limit of Woodin cardinals λ. In particular, we prove that two-step ∃R(Π ̃ 1)λ generic absoluteness below a measurable cardinal that is a limit of Woodin cardinals has high consistency strength, and that it is equivalent with the existence of ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06465-1