Shift spaces, Languages and Transfinite Induction

Maira Aranguren, Jorge Campos, Neptalí Romero, Ramón Vivas

Published 2023-08-20Version 1

This note deal with an extension of the classical notion of shift space: shift-invariant closed subsets of a Cartesian product of finite sets endowed with the prodiscrete topology. In such a framework it is introduced the language of this type of shift space and a characterization is shown, which requires transfinite induction because the universe of those shift spaces are not necessarily countable.