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Bases and borel selectors for tall families

Jan Grebík & Carlos Uzcátegui

Journal of Symbolic Logic 84 (1):359-375 (2019)

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Katětov order on Borel ideals.Michael Hrušák - 2017 - Archive for Mathematical Logic 56 (7-8):831-847.details We study the Katětov order on Borel ideals. We prove two structural theorems, one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals. Download Export citation Bookmark 15 citations
An effective proof that open sets are Ramsey.Jeremy Avigad - 1998 - Archive for Mathematical Logic 37 (4):235-240.details Solovay has shown that if $\cal{O}$ is an open subset of $P(\omega)$ with code $S$ and no infinite set avoids $\cal{O}$ , then there is an infinite set hyperarithmetic in $S$ that lands in $\cal{O}$ . We provide a direct proof of this theorem that is easily formalizable in $ATR_0$. Download Export citation Bookmark 8 citations
Ramsey type properties of ideals.M. Hrušák, D. Meza-Alcántara, E. Thümmel & C. Uzcátegui - 2017 - Annals of Pure and Applied Logic 168 (11):2022-2049.details Download Export citation Bookmark 10 citations

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