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arXiv · 2308.10352

Shift spaces, Languages and Transfinite Induction

Maira Aranguren·Jorge Campos·Neptalí Romero·Ramón Vivas
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Abstract

This paper deals with an extension of the classical concept of shift space, which corresponds to any shift-invariant closed subset of the Cartesian product of a particular finite set (alphabet) endowed with the prodiscrete topology. In such an extended framework the notion of language is introduced and a characterization is shown. In order to do this, transfinite induction is required because the cardinality of the index set of the product may not be countable.

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Maira Aranguren, Jorge Campos, Neptalí Romero, Ramón Vivas. 2023-08-20. Shift spaces, Languages and Transfinite Induction. https://arxiv.org/abs/2308.10352

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