A small Boolean algebra that is Grothendieck but not Nikodym, part II

Speaker(s)

Damian Głodkowski

Affiliation

UW

Language of the talk

English

Date

Dec. 18, 2024, 4:15 p.m.

Room

room 5050

Title in Polish

A small Boolean algebra that is Grothendieck but not Nikodym, part II

Seminar

Topology and Set Theory Seminar

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The talk will be devoted to the Grothendieck and Nikodym properties concerning measures on Boolean algebras. In 1984 Talagrand showed that under the continuum hypothesis there is a Boolean algebra with the Grothendieck property and without the Nikodym property, but the problem of the existence of such an algebra is still open in ZFC. I will discuss the main ideas behind Talagrand's construction and show how to modify them to obtain a notion of forcing that forces the existence of a Boolean algebra of cardinality $\omega_1$, which has the Grothendieck property, but does not have the Nikodym property. Our forcing preserves cardinals and the value of the continuum, so in particular, the existence of such an algebra is consistent with any possible value of the continuum.
The talk will be based on joint work with Agnieszka Widz: https://doi.org/10.1016/j.jfa.2024.110757

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