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Analytic Equivalence Relations and the Forcing Method

Jindřich Zapletal

Bulletin of Symbolic Logic 19 (4):473-490 (2013)

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Covering analytic sets by families of closed sets.Sławomir Solecki - 1994 - Journal of Symbolic Logic 59 (3):1022-1031.details We prove that for every family I of closed subsets of a Polish space each Σ 1 1 set can be covered by countably many members of I or else contains a nonempty Π 0 2 set which cannot be covered by countably many members of I. We prove an analogous result for κ-Souslin sets and show that if A ♯ exists for any $A \subset \omega^\omega$ , then the above result is true for Σ 1 2 sets. A theorem (...) Download Export citation Bookmark 5 citations
Dominating and unbounded free sets.Slawomir Solecki & Otmar Spinas - 1999 - Journal of Symbolic Logic 64 (1):75-80.details We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective. Download Export citation Bookmark 5 citations

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