Compactness of Powers of $ \omega $
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 239-246
MSC: Primary 54B10, 54D20, 03C75; Secondary 03C20, 03E05, 54A20, 54A25.
DOI: 10.4064/ba61-3-5
Abstract
We characterize exactly the compactness properties of the product of $\kappa $ copies of the space $ \omega $ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.
