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Shows that certain effective subshifts do not correlate with any effective dynamical systems, implying new insights into their properties.
We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts, whose inverse limit is not the topological factor of any effective dynamical system. This follows from considerations on the universality under topological factors for this class of dynamical systems.
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Barbieri et al. (2026) studied this question.
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