Evasion and prediction II

Abstract

A subgroup G \leq Z^omega exhibits the Specker phenomenon if every homomorphism G \to Z maps almost all unit vectors to 0. We give several combinatorial characterizations of the cardinal se, the size of the smallest G \leq Z^omega exhibiting the Specker phenomenon. We also prove the consistency of b < e, where b is the unbounding number and e the evasion number introduced recently by Blass. Finally we show that e \geq \min { aleph_0--e , cov(M) }, where aleph_0--e is the aleph_0--evasion number (the uniformity of the evasion ideal) and cov(M) is the covering number of the meager ideal. All these results can be dualized. They answer several questions addressed by Blass.