Abstract

Extending some results of Malykhin, we prove several independence results about base properties of βω \ ω and its powers, especially the Noetherian type Nt(βω \ ω), the least κ for which βω \ ω has a base that is κ-like with respect to containment. For example, Nt(βω \ ω) is at least s, but can consistently be ω1, c, cT, or strictly between ω1 and c. Nt(βω \ ω) is also consistently less than the additivity of the meager ideal. Nt(βω \ ω) is closely related to the existence of spcial kinds of splitting families