On measures induced by forcing names for ultrafilters

Borodulin–Nadzieja, Piotr; Cegiełka, Katarzyna

doi:10.1016/j.topol.2022.108278

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Pointwise Borel Metric Topology and Uniform Borel Topology1

A Sequence Which Is Pointwise Borel Metric Convergent and Po...1

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Cited by 1 publication

(2 citation statements)

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“…By the Nikodym Convergence Theorem, the sequence is uniformly countably additive, so the conclusion follows by Proposition 4. 4.…”

Section: Pointwise Borel Metric Topology and Uniform Borel Topologymentioning

confidence: 99%

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On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem

Borodulin–Nadzieja¹,

Sobota²

2021

J. symb. log.

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For given Boolean algebras $\mathbb {A}$ and $\mathbb {B}$ we endow the space $\mathcal {H}(\mathbb {A},\mathbb {B})$ of all Boolean homomorphisms from $\mathbb {A}$ to $\mathbb {B}$ with various topologies and study convergence properties of sequences in $\mathcal {H}(\mathbb {A},\mathbb {B})$ . We are in particular interested in the situation when $\mathbb {B}$ is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on $\mathbb {A}$ in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating that there are Efimov spaces in the random model. We also investigate relations between topologies on $\mathcal {H}(\mathbb {A},\mathbb {B})$ for a Boolean algebra $\mathbb {B}$ carrying a strictly positive measure and convergence properties of sequences of measures on $\mathbb {A}$ .

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“…By the Nikodym Convergence Theorem, the sequence is uniformly countably additive, so the conclusion follows by Proposition 4. 4.…”

Section: Pointwise Borel Metric Topology and Uniform Borel Topologymentioning

confidence: 99%

“…A study of the interplay between the properties of M κ -names for ultrafilters and measures is a subject of forthcoming paper [4].…”

Section: A Sequence Which Is Pointwise Borel Metric Convergent and Po...mentioning

confidence: 99%

On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem

Borodulin–Nadzieja¹,

Sobota²

2021

J. symb. log.

View full text Add to dashboard Cite

show abstract

On measures induced by forcing names for ultrafilters

Cited by 1 publication

References 27 publications

On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem

On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem

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