A+ CATEGORY SCIENTIFIC UNIT

Quasi-bounded trees and analytic inductions

Volume 191 / 2006

Jean Saint Raymond Fundamenta Mathematicae 191 (2006), 175-185 MSC: 03E15, 54H05. DOI: 10.4064/fm191-2-4

Abstract

A tree $T$ on $\omega $ is said to be cofinal if for every $\alpha \in \omega ^\omega $ there is some branch $\beta $ of $T$ such that $\alpha \leq \beta $, and quasi-bounded otherwise. We prove that the set of quasi-bounded trees is a complete ${\bf\Sigma }^1_1$-inductive set. In particular, it is neither analytic nor co-analytic.

Authors

  • Jean Saint RaymondAnalyse Fonctionnelle
    Institut de Mathématique de Jussieu
    Boîte 186
    4, place Jussieu
    75252 Paris Cedex 05, France
    e-mail

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