A syntactic approach to Borel functions: Some extensions of Louveau's theorem
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 extensiontype, dominationtype, and decompositiontype variants of Louveau's theorem for Borel functions.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.02950
 Bibcode:
 2021arXiv210302950K
 Keywords:

 Mathematics  Logic