Damjan Kalajdzievski, Juris Steprāns
Uniqueness of means in the Cohen model

Comment.Math.Univ.Carolin. 60,1 (2019) 49-60.

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