Abstract:We investigate the question of whether or not an amenable subgroup of the permutation group on $\mathbb{N}$ can have a unique invariant mean on its action. We extend the work of M.\ Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.
Keywords: construction scheme; Knaster hierarchy; Cohen reals
DOI: DOI 10.14712/1213-7243.2015.274
AMS Subject Classification: 03E05 03E35 03E65