A remark on inverse limits of effective subshifts

TL;DR

This paper demonstrates that for certain groups with specific decision problems, there exist effective subshifts whose inverse limits cannot be realized as factors of any effective dynamical system, highlighting limitations in universality.

Contribution

It establishes the existence of effective subshifts with inverse limits that are not topological factors of any effective dynamical system for groups with decidable word problem and undecidable domino problem.

Findings

Inverse limits of certain effective subshifts are not factors of any effective dynamical system.

Universality under topological factors is limited for these classes of dynamical systems.

Results depend on properties of the underlying finitely generated groups.

Abstract

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.