On a question of Andreas Weiermann

摘要

We prove that for each beta, gamma < epsilon(o) there exists alpha < epsilon(0) such that whenever A subset of w is alpha-large and G : A -> beta is such that (for all a is an element of A)(psn(G(a)) <= a), then there exists gamma-large C subset of A on which G is nondecreasing. Moreover, we give upper bounds for a for small ordinals beta <= w(ww).