Sobota, D., & Zdomskyy, L. (2024). Convergence of measures after adding a real. Archive for Mathematical Logic, 63, 135–162. https://doi.org/10.1007/s00153-023-00888-0
Convergence of measures; Forcing; Grothendieck property; Nikodym property
en
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.
