Borel's conjecture and meager-additive sets

2020/12/04 by Calderón, Daniel
#03E15. Secondary: 54F65 #03E75 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Primary: 03E35

paper · doi:10.48550/arxiv.2012.02396

Abstract

We prove that it is relatively consistent with ZFC that every strong measure zero subset of the real line is meager-additive while there are uncountable strong measure zero sets (i.e., Borel's conjecture fails). This answers a long-standing question due to Bartoszyński and Judah.

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