L-SPACES AND THE P-IDEAL DICHOTOMY

We extend a theorem of Todorcevic: Under the assumption (K) (see Definition 1.11), boxed times {any regular space Z with countable tightness such that Z(n) is Lindelof for all n epsilon omega has no L-subspace. We assume p > omega(1) and a weak form of Abraham and Todorcevic's P-ideal dichotomy instead and get the same conclusion. Then we show that p > omega(1) and the dichotomy principle for P-ideals that have at most aleph(1) generators together with boxed times do not imply that every Aronszajn tree is special, and hence do not imply (K). So we really extended the mentioned theorem.