• Corpus ID: 232110437

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

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