منابع مشابه
Strongly meager sets of size continuum
We will construct several models where there are no strongly meager sets of size 2 ℵ 0 .
متن کاملStrongly Meager Sets Are Not an Ideal
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.
متن کاملStrongly meager sets and subsets of the plane
Let X ⊆ 2 . Consider the class of all Borel F ⊆ X × 2 with null vertical sections Fx, x ∈ X. We show that if for all such F and all null Z ⊆ X, ⋃ x∈Z Fx is null, then for all such F , ⋃ x∈X Fx 6= 2 . The theorem generalizes the fact that every Sierpiński set is strongly meager and was announced in [P]. A Sierpiński set is an uncountable subset of 2 which meets every null (i.e., measure zero) se...
متن کاملStrongly Meager Sets and Their Uniformly Continuous Images
We prove the following theorems: (1) Suppose that f : 2ω → 2ω is a continuous function and X is a Sierpiński set. Then (A) for any strongly measure zero set Y , the image f [X + Y ] is an s0-set, (B) f [X] is a perfectly meager set in the transitive sense. (2) Every strongly meager set is completely Ramsey null. This paper is a continuation of earlier works by the authors and by M. Scheepers (s...
متن کاملStrongly Meager Sets Do Not Form an Ideal
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: Archive for Mathematical Logic
سال: 2003
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-003-0184-0