Quasi-bounded trees and analytic inductions
Volume 191 / 2006
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.
