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

· 2021 · math.LO · arXiv 2107.09866

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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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Dynamical pair assignments

math.DS · 2025-01-22 · conditional · novelty 6.0

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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  • Dynamical pair assignments math.DS · 2025-01-22 · conditional · none · ref 5 · internal anchor

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