We prove that there exist arbitrarily long arithmetic progressions in a subset of an amenable group $\Gamma\supseteq\mathbb{Z}$ with positive upper density with respect to a F{\o}lner sequence. This generalizes Szemer\'edi's theorem to amenable groups.
An embedding theorem for subshifts over amenable groups with the comparison property
Minimal models for actions of amenable groups
Symbolic dynamics on amenable groups: the entropy of generic shifts
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