• Corpus ID: 238583592

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
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 in the Sacks model
Abstract We prove that if A is a σ -complete Boolean algebra in a ground model V of set theory, then A has the Nikodym property in every side-by-side Sacks forcing extension V [ G ] , i.e. every
The Nikodym property and cardinal characteristics of the continuum
  • Damian Sobota
  • Computer Science, Mathematics
    Ann. Pure Appl. Log.
  • 2019
TLDR
A consistent example of an infinite Boolean algebra with the Nikodym property and of cardinality strictly less than the continuum c is obtained, it follows that the existence of such an algebra is undecidable by the usual axioms of set theory.
Minimally generated Boolean algebras and the Nikodym property
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
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
Small cardinals and small Efimov spaces
  • W. Brian, A. Dow
  • Computer Science, Mathematics
    Ann. Pure Appl. Log.
  • 2022
TLDR
A new cardinal characteristic of the continuum, the splitting number of the reals, is introduced and analyzed, connected to Efimov's problem, which asks whether every infinite compact Hausdorff space must contain either a non-trivial convergent sequence, or else a copy of $\beta \mathbb N$.
Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole
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
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
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
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
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