A note on derivatives, expansions and Π¹₁-ranks

2021/07/21 by Udayan B. Darji, Felipe García‐Ramos, Darji, Udayan B. +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2107.09866

openalex publication_date 2021/07/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Π₁¹-ranks are a natural tool for studying coanalytic sets in descriptive set theory. In the book "Classical descriptive set theory", Kechris provided a technique to build Π₁¹-ranks using derivatives. In this note we will prove a variant of this result that is applicable to the Γ-rank. Some dynamical ranks, like the entropy rank can be stated in terms of the Γ-rank.

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