On the structure of the Wadge degrees of bqo-valued Borel functions
Takayuki Kihara, Antonio Montalbán · Transactions of the American Mathematical Society · 2018
In this article, we give a full description of the Wadge degrees of Borel functions from $\omega ^\omega$ to a better-quasi-ordering $\mathcal {Q}$. More precisely, for any countable ordinal $\xi$, we show that the Wadge degrees of $\mathbf {\Delta }^0_{1+\xi }$-measurable functions $\omega ^\omega \to \mathcal {Q}$ can be represented by countable joins of the $\xi$th transfinite nests of $\mathcal {Q}$-labeled well-founded trees.