An upper bound on the complexity of recognizable tree languages

@article{Finkel2015AnUB,
  title={An upper bound on the complexity of recognizable tree languages},
  author={Olivier Finkel and Dominique Lecomte and Pierre Simonnet},
  journal={ArXiv},
  year={2015},
  volume={abs/1503.02840}
}
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this… 

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