We characterize exactly the compactness properties of the product of κ copies of the space ω 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-5,
author = {Paolo Lipparini},
title = {Compactness of Powers of $\omega$},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {61},
year = {2013},
pages = {239-246},
zbl = {1298.54009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-5}
}
Paolo Lipparini. Compactness of Powers of ω. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 239-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-5/