Cohen real or random real: effect on strong measure zero sets and strongly meager sets

2020/05/16 by Cardona, Miguel A.
#03E05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2005.07912

Abstract

We show that the set of the ground-model reals has strong measure zero (is strongly meager) after adding a single Cohen real (random real). As consequence we prove that the set of the ground-model reals has strong measure zero after adding a single Hechler real.

Related

• Strongly meager and strong measure zero sets
• Strong measure zero and meager-additive sets through the prism of fractal measures
• Small forcings and Cohen reals
• Universally meager sets in the Miller model and similar ones
• Borel's conjecture and meager-additive sets