Borel’s conjecture and meager-additive sets
نویسندگان
چکیده
We prove that it is relatively consistent with $\mathrm{ZFC}$ every strong measure zero subset of the real line meager-additive while there are uncountable sets (i.e., Borel's conjecture fails). This answers a long-standing question due to Bartoszynski and Judah.
منابع مشابه
Every null - additive set is meager - additive †
§1. The basic definitions and the main theorem. 1. Definition. (1) We define addition on 2 as addition modulo 2 on each component, i.e., if x, y, z ∈ 2 and x+ y = z then for every n we have z(n) = x(n) + y(n) (mod 2). (2) For A,B ⊆ 2 and x ∈ 2 we set x + A = {x + y : y ∈ A}, and we define A + B similarly. (3) We denote the Lebesgue measure on 2 with μ. We say that X ⊆ 2 is null-additive if for ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15536