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  1.  22
    Convergence of measures after adding a real.Damian Sobota & Lyubomyr Zdomskyy - 2023 - Archive for Mathematical Logic 63 (1):135-162.
    We prove that if $$\mathcal {A}$$ A is an infinite Boolean algebra in the ground model V and $$\mathbb {P}$$ 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 $$\mathbb {P}$$ P -generic extension V[G], $$\mathcal {A}$$ A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.
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  2.  10
    On Sequences of Homomorphisms Into Measure Algebras and the Efimov Problem.Piotr Borodulin–Nadzieja & Damian Sobota - 2023 - Journal of Symbolic Logic 88 (1):191-218.
    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 (...)
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  3.  14
    The Nikodym property and cardinal characteristics of the continuum.Damian Sobota - 2019 - Annals of Pure and Applied Logic 170 (1):1-35.
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  4.  12
    The Josefson–Nissenzweig theorem and filters on $$\omega $$.Witold Marciszewski & Damian Sobota - forthcoming - Archive for Mathematical Logic:1-40.
    For a free filter F on $$\omega $$ ω, endow the space $$N_F=\omega \cup \{p_F\}$$ N F = ω ∪ { p F }, where $$p_F\not \in \omega $$ p F ∉ ω, with the topology in which every element of $$\omega $$ ω is isolated whereas all open neighborhoods of $$p_F$$ p F are of the form $$A\cup \{p_F\}$$ A ∪ { p F } for $$A\in F$$ A ∈ F. Spaces of the form $$N_F$$ N F constitute the (...)
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  5.  18
    Families of sets related to Rosenthal’s lemma.Damian Sobota - 2019 - Archive for Mathematical Logic 58 (1-2):53-69.
    A family \ is called Rosenthal if for every Boolean algebra \, bounded sequence \ of measures on \, antichain \ in \, and \, there exists \ such that \<\varepsilon \) for every \. Well-known and important Rosenthal’s lemma states that \ is a Rosenthal family. In this paper we provide a necessary condition in terms of antichains in \}\) for a family to be Rosenthal which leads us to a conclusion that no Rosenthal family has cardinality strictly less (...)
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