Infinitely many minimal subsystems in universal symbolic systems

A universal symbolic system is a symbolic dynamical system capable of simulating every effective symbolic system. Universality conjecture. Every universal symbolic system has infinitely many minimal subsystems. This conjecture identifies a proposed structural consequence of universality and concerns the boundary between decidability and more general symbolic dynamics; the supplied text gives no resolution.

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Primary source

Ville Salo, “Decidability and Universality of Quasiminimal Subshifts”, arXiv:1411.6644 (2015).

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