Smooth digraphs of algebraic length 1 pp-construct all finite structures unless they have a pseudo-loop, yielding the first hardness criterion for infinite directed graph colouring.
Now, (µ 1 +µ 2 +µ 3,µ ′ 1 +µ ′ 2 +µ ′ 3) has the required properties
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The sorrows of a smooth digraph: the first hardness criterion for infinite directed graph-colouring problems
Smooth digraphs of algebraic length 1 pp-construct all finite structures unless they have a pseudo-loop, yielding the first hardness criterion for infinite directed graph colouring.