Compactness of ${\omega }^{\lambda }$ for $\lambda$ singular

Abstract

We characterize the compactness properties of the product of λ copies of the space ω with the discrete topology, dealing in particular with the case λ singular, using regular and uniform ultrafilters, infinitary languages and nonstandard elements. We also deal with products of uncountable regular cardinals with the order topology.

Treats the case λ singular only hinted in arXiv:1302.4763; v2 some very minor improvements and corrections