English

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

Logic 2021-07-22 v1 Dynamical Systems

Abstract

Π11\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 Π11\Pi_1^1-ranks using derivatives. In this note we will prove a variant of this result that is applicable to the Γ\Gamma-rank. Some dynamical ranks, like the entropy rank can be stated in terms of the Γ\Gamma-rank.

Keywords

Cite

@article{arxiv.2107.09866,
  title  = {A note on derivatives, expansions and $\Pi^1_1$-ranks},
  author = {Udayan B. Darji and Felipe García-Ramos},
  journal= {arXiv preprint arXiv:2107.09866},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2107.09263