Hereditarily nonparadoxical sets revisited

摘要

We prove that assuming c ＜ N_ω every translation - hereditarily nonparadoxical subset of R~1 is a countable sum of sets without repeated differences. In particular, under the same assumption every hereditarily nonparadoxical subset of the real line is a countable sum of sets without repeated distances. This gives a partial answer to the question of M. Penconek from.