# A syntactic approach to Borel functions: Some extensions of Louveau's theorem

@inproceedings{Kihara2021ASA, title={A syntactic approach to Borel functions: Some extensions of Louveau's theorem}, author={Takayuki Kihara and Kenta Sasaki}, year={2021} }

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 ̃ t-function, then one can effectively find its ̃ 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…

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