Evasion and prediction II

A subgroup G ≤ ℤ^ω exhibits the Specker phenomenon if every homomorphism G → ℤ maps almost all unit vectors to 0. We give several combinatorial characterizations of the cardinal s-fraktur signe, the size of the smallest G ≤ ℤ^ω exhibiting the Specker phenomenon. We also prove the consistency of b < e, where b is the unbounding number and e the evasion number. Our results answer several questions addressed by Blass.