On the existence of large subsets of [λ] κ which contain no unbounded non-stationary subsets

Abstract

Here we deal with some problems posed by Matet. The first section deals with the existence of stationary subsets of [λ]<κ with no unbounded subsets which are not stationary, where, of course, κ is regular uncountable ≤λ. In the second section we deal with the existence of such clubs. The proofs are easy but the result seems to be very surprising. Theorem 1.2 was proved some time ago by Baumgartner (see Theorem 2.3 of [Jo88]) and is presented here for the sake of completeness.