Partitioning products of 𝒫(ω)∕fin

Otmar Spinas

Vol. 176 (1996), No. 1, 249–262

DOI: 10.2140/pjm.1996.176.249

Abstract

We generalize the cardinal invariant a to products of 𝒫(ω)∕fin and then sharpen the well-known inequality b ≤ a by proving b ≤ a(λ) for every λ ≤ ω. Here a(n), for n < ω, is the least size of an infinite partition of (𝒫(ω)∕fin)ⁿ, a(ω) is the least size of an uncountable partition of (𝒫(ω)∕fin)^ω, and b is the least size of an unbounded family of functions from ω to ω ordered by eventual dominance. We also prove the consistency of b < a(n) for every n < ω.

Mathematical Subject Classification 2000

Primary: 03E05

Secondary: 03E35

Milestones

Received: 22 September 1994

Revised: 11 January 1995

Published: 1 November 1996