• Corpus ID: 232110437

# 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}
}
• Published 4 March 2021
• Mathematics
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…

## References

SHOWING 1-10 OF 40 REFERENCES
A Wadge hierarchy for second countable spaces
A notion of reducibility for subsets of a second countable T0 topological space based on relatively continuous relations and admissible representations is defined and induces a hierarchy that refines the Baire classes and the Hausdorff–Kuratowski classes of differences.
A separation theorem for Σ11
• sets. Trans. Amer. Math. Soc.,
• 1980
Decomposing Borel functions using the Shore-Slaman join theorem
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the
A Q-WADGE HIERARCHY IN QUASI-POLISH SPACES
Abstract The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). Here we extend the Wadge hierarchy of Borel sets to arbitrary
Descriptive Complexity on Non-Polish Spaces
• Mathematics
STACS
• 2020
This investigation is aimed at explaining the difference in descriptive complexity of subsets of represented spaces and highly suggests that it is related to the well-known mismatch between topological and sequential aspects of topological spaces.
Wadge-like degrees of Borel bqo-valued functions
• Mathematics
ArXiv
• 2019
The main result states that the structure of the $\mathbf{\Delta}^0_\alpha$-degrees of $Q$-measurable $Q-valued functions is isomorphic to the generalized homomorphism order on the$\gamma\$-th iterated £Q-labeled forests.