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arXiv · 1411.6644

Decidability and Universality of Quasiminimal Subshifts

Ville Salo
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Abstract

We introduce the quasiminimal subshifts, subshifts having only finitely many subsystems. With $\mathbb{N}$-actions, their theory essentially reduces to the theory of minimal systems, but with $\mathbb{Z}$-actions, the class is much larger. We show many examples of such subshifts, and in particular construct a universal system with only a single proper subsystem, refuting a conjecture of [Delvenne, K\r{u}rka, Blondel, '05].

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Ville Salo. 2014-11-24. Decidability and Universality of Quasiminimal Subshifts. https://arxiv.org/abs/1411.6644

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