# Convergence of measures after adding a real

@inproceedings{Sobota2021ConvergenceOM, title={Convergence of measures after adding a real}, author={Damian Sobota and Lyubomyr Zdomskyy}, year={2021} }

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.

## References

SHOWING 1-10 OF 37 REFERENCES

Convergence of measures in forcing extensions

- MathematicsIsrael Journal of Mathematics
- 2019

We prove that if A is a σ-complete Boolean algebra in a model V of set theory and ℙ ∈ V is a proper forcing with the Laver property preserving the ground model reals non-meager, then every pointwise…

The Nikodym property and cardinal characteristics of the continuum

- MathematicsAnn. Pure Appl. Log.
- 2019

Minimally generated Boolean algebras and the Nikodym property

- Mathematics
- 2021

A Boolean algebra A has the Nikodym property if every pointwise bounded sequence of bounded finitely additive measures on A is uniformly bounded. Assuming the Diamond Principle ♦, we will construct…

COMPACT SETS WITHOUT CONVERGING SEQUENCES IN THE RANDOM REAL MODEL

- Mathematics
- 2000

It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdor space of weight !1 which contains no non-trivial converging sequences. It is…

Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole

- Mathematics
- 1988

In this paper the relations between some properties of interpolation and some properties of supremum, on Boolean algebras with the countable chain condition, are studied. It is also proved that a…

BOOLEAN RINGS THAT ARE BAIRE SPACES

- Mathematics
- 2001

Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions…

TOOLS FOR YOUR FORCING CONSTRUCTION

- Mathematics
- 1992

A preservation theorem is a theorem of the form: "If hP�,Q� : � < �i is an iteration of forcing notions, and every Qsatisfies ' in V P� , then Psatisfies '." We give a simplified version of a general…

On the density of Banach spaces C(K) with the Grothendieck property

- Mathematics
- 2006

Using the method of forcing we prove that consistently there is a Banach space of continuous functions on a compact Hausdorff space with the Grothendieck property and with density less than the…