A syntactic approach to Borel functions: Some extensions of Louveau's theorem [article]

Takayuki Kihara, Kenta Sasaki
2021 arXiv   pre-print
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 Σ_t-function, then one can effectively find its Σ_t-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.
arXiv:2103.02950v1 fatcat:q6khftebuzbwtaww2c4bmwvkia