Ideals with Smital properties

Autor: Marcin Michalski, Robert Rałowski, Szymon Żeberski
Rok vydání: 2023
Předmět:
Zdroj: Archive for Mathematical Logic. 62:831-842
ISSN: 1432-0665
0933-5846
Popis: A $$\sigma $$ σ -ideal $$\mathcal {I}$$ I on a Polish group $$(X,+)$$ ( X , + ) has the Smital Property if for every dense set D and a Borel $$\mathcal {I}$$ I -positive set B the algebraic sum $$D+B$$ D + B is a complement of a set from $$\mathcal {I}$$ I . We consider several variants of this property and study their connections with the countable chain condition, maximality and how well they are preserved via Fubini products. In particular we show that there are $$\mathfrak {c}$$ c many maximal invariant $$\sigma $$ σ -ideals with Borel bases on the Cantor space $$2^\omega $$ 2 ω .
Databáze: OpenAIRE
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