Weakly Compact Cardinals and Nonspecial Aronszajn Trees

Abstract

ABSTRACT. LEMMA 1. If X is a cardinal with cf A > u>, then Dx implies that there is a A+-Aronszajn tree with an ui-ascent path, i.e. a sequence (xa : a < A+) with each xa = (i" : n < ui) a one-to-one sequence from Ta, such that for all a < ß < A+, z° precedes x" in the tree order for sufficiently large n.