Universally meager sets, II
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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We show that it is consistent that the product of perfectly meager sets is perfectly meager.
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Using ♦ and large cardinals we extend results of Magidor–Malitz and Farah–Larson to obtain models correct for the existence of uncountable homogeneous sets for finite-dimensional partitions and universally Baire sets. Furthermore, we show that the constructions in this paper and its predecessor can be modified to produce a family of 2ω1 -many such models so that no two have a stationary, costat...
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We will construct several models where there are no strongly meager sets of size 2 ℵ 0 .
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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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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2008
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.05.005