Regularity properties for dominating projective sets

Brendle, Jörg; Hjorth, Greg; Spinas, Otmar

doi:10.1016/0168-0072(94)00027-z

Cited by 15 publications

(73 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Call a set C ⊆ ω ω nice if for some ((w σ , s σ ) : σ ∈ ω <ω ) ∈ S, C = {y ∈ ω ω : s ∅ ⊆ y and ∃x ∈ ω ω ∀n ∈ ω (y|w x|n = s x|n+1 )}. Now [BHS,Theorem 1.1] implies that a closed set is dominating precisely when it contains a nice set. Therefore,…”

Section: Complexity Of Closed Haar Null Sets and Other Applicationsmentioning

confidence: 99%

Haar null and non-dominating sets

Solecki¹

2001

Fund. Math.

View full text Add to dashboard Cite

We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of ω ω. Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain results connecting Haar null sets on countable products of locally compact Polish groups with amenability of the factor groups.

show abstract

Section: Complexity Of Closed Haar Null Sets and Other Applicationsmentioning

confidence: 99%

Haar null and non-dominating sets

Solecki¹

2001

Fund. Math.

View full text Add to dashboard Cite

show abstract

“…" Va £ co w (Hech(L[«]) € (d 1 )) <=$ V«Gffl f f l {x\ [a] < Ni). From [2] we introduce the following notion: We are now ready to complete the proof of Theorem 6.1. We form A := { y G o3 m : min{ a : 7 <* / a } is even }, 5 := { y e m m : min{ a : y <* f a }is odd }.…”

Section: ^:= U ^-mentioning

confidence: 99%

“…We sketch another connection between two regularity properties which we shall need in Section 4 when dealing with Laver forcing. To this end, we introduce the following three notions the first of which is Definition 2.1 in [4] while the last is on p. 296 in [2]: To see that B is dominating, let g e co m be an arbitrary increasing function such that <p(g)(j -1) > j for all j . Find x € A such that x(n + 1) > <p(g)(x(n)) for all n e co.…”

mentioning

confidence: 99%

Solovay-type characterizations for forcing-algebras

Brendle

Löwe

1999

J. symb. log.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The subsets of ω ω which are not cofinal will also be called quasi-bounded. The structure of cofinal subsets of ω ω was already studied by several people (see [5], [1] or [2]). The aim of this paper is to prove that the set QB of quasi-bounded trees on ω is a Σ 0 2 -complete subset of T .…”

Section: Sequences and Treesmentioning

confidence: 99%

Quasi-bounded trees and analytic inductions

Raymond

2006

Fund. Math.

View full text Add to dashboard Cite

Abstract.A tree T on ω is said to be cofinal if for every α ∈ ω ω there is some branch β of T such that α ≤ β, and quasi-bounded otherwise. We prove that the set of quasi-bounded trees is a complete Σ 1 1 -inductive set. In particular, it is neither analytic nor co-analytic.In a recent joint work with G. Debs, we were led to study the complexity of the set of cofinal trees as a subset of the compact set of all trees on ω, in fact to show that this set is not Π 1 1 . The aim of this paper is to compute the exact complexity of this set, which appears to be beyond the σ-algebra generated by the analytic sets. We also prove similar results concerning the set of cofinal or quasi-bounded closed subsets of the Baire space with respect to the Effros Borel structure on the set F (ω ω ) of closed nonempty subsets of ω ω . Most of the definitions and results we recall here can be found in [4], which we refer to for all undefined notions and basic properties of classical descriptive classes. Sequences and trees.For any set E we denote by Seq(E) the set of finite sequences of elements of E. If s = e 0 , e 1 , . . . , e k−1 ∈ Seq(E) we denote by |s| its length k. As usual, for any two s = e 0 , e 1 , . . . , e k−1 and t = a 0 , a 1 , . . . , a l−1 in Seq(E) we say that t extends s or that s is a beginning of t, and write s ≺ t if |s| < |t| and e i = a i for i < |s|. And we write s t iff s ≺ t or s = t. When s ∈ Seq(E) and k ≤ |s|, we denote by s |k the sequence

show abstract

Regularity properties for dominating projective sets

Cited by 15 publications

References 12 publications

Haar null and non-dominating sets

Haar null and non-dominating sets

Solovay-type characterizations for forcing-algebras

Quasi-bounded trees and analytic inductions

Contact Info

Product

Resources

About