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Complete pairs of coanalytic sets

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Raymond J.

Fundamenta Mathematicae

2007

tom 194

nr 3

267-281

Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of $ω^{ω}$ there exists a continuous function $f: ω^{ω} → X$ such that $f^{-1}(C₀) = D₀$ and $f^{-1}(C₁) = D₁$. We give several explicit examples of complete pairs of coanalytic sets.

Quasi-bounded trees and analytic inductions

100%

Raymond J.

Fundamenta Mathematicae

2006

tom 191

nr 2

175-185

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 Σ¹₁-inductive set. In particular, it is neither analytic nor co-analytic.

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2 Fundamenta Mathematicae

2 Raymond J.

1 2007

1 2006

Wyniki wyszukiwania

Complete pairs of coanalytic sets

Quasi-bounded trees and analytic inductions