Convergence of measures after adding a real

2021/10/09 by Damian Sobota, Sobota, Damian, Lyubomyr Zdomskyy +1 · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Algebra and Logic #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2110.04568

Abstract

We prove that if A is an infinite Boolean algebra in the ground model V and ℙ is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any ℙ-generic extension V[G], A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.

Cited by

• The Nikodym and Grothendieck properties of Boolean algebras and rings related to ideals

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