Null-additive sets and the property gamma

Speaker(s)

Piotr Szewczak

Affiliation

Cardinal Wyszyński University in Warsaw

Date

Dec. 11, 2019, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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A subset X of the real line is null-additive if for each null set Y, the set X+Y is null. Under Martin Axiom, Galvin nad Miller constructed an uncountable null-additive set whose continuous images are also null-additive; this set has the property gamma, a strong combinatorial covering property. Bartoszyński and Recław proved that, assuming p=c, there is a gamma set that is not null additive. The aim of the talk is to construct sets with the above properties, using weaker set-theoretic assumptions. This is a joint work with Tomasz Weiss.

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