Wadge-like degrees of Borel bqo-valued functions

2019/09/24 by Takayuki Kihara, Kihara, Takayuki, Victor Selivanov +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1909.10835

openalex publication_date 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e., \0,1\-valued functions) to Q-valued functions, for a better quasiorder Q. In this article, we consider more general reducibilities on the Q-valued functions and generalise some results of L. Motto Ros in the first direction and of T. Kihara and A. Montalbán in the second direction: Our main result states that the structure of the \mathbfΔ⁰_α-degrees of \mathbfΔ⁰_α+γ-measurable Q-valued functions is isomorphic to the \mathbfΔ⁰_β-degrees of \mathbfΔ⁰_β+γ-measurable Q-valued functions, and these are isomorphic to the generalized homomorphism order on the γ-th iterated Q-labeled forests.

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