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

Takayuki Kihara; Kenta Sasaki

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arXiv · 2103.02950

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

Takayuki Kihara·Kenta Sasaki

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Abstract

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $\Gamma$, then its $\Gamma$-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 $\Sigma_t$-function, then one can effectively find its $\Sigma_t$-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.

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BibTeX RIS

Takayuki Kihara, Kenta Sasaki. 2021-03-04. A syntactic approach to Borel functions: Some extensions of Louveau's theorem. https://arxiv.org/abs/2103.02950

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