2021/03/04 by Kihara, Takayuki, Sasaki, Kenta
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2103.02950
Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class Γ, then its Γ-code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau's theorem to Borel functions: If a Borel function on a Polish space happens to be a Σt-function, then one can effectively find its Σt-code hyperarithmetically relative to its Borel code. More generally, we prove extension-type, domination-type, and decomposition-type variants of Louveau's theorem for Borel functions.