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A note on derivatives, expansions and $\Pi^1_1$-ranks

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arxiv 2107.09866 v1 pith:SR7EDDA3 submitted 2021-07-21 math.LO math.DS

Udayan B. Darji , Felipe García-Ramos This is my paper · ORCID
classification math.LOmath.DS
keywords ranksrankderivativesdescriptivegammanotetheoryapplicable
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abstract

$\Pi_1^1$-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 $\Pi_1^1$-ranks using derivatives. In this note we will prove a variant of this result that is applicable to the $\Gamma$-rank. Some dynamical ranks, like the entropy rank can be stated in terms of the $\Gamma$-rank.

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  1. Dynamical pair assignments

    math.DS 2025-01 conditional novelty 6.0 of 10

    Introduces dynamical pair assignments and proves the space of P-realizable systems is Borel if and only if the associated P-rank is bounded.

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