Compactness of $\omega^\lambda$ for $\lambda$ singular
Paolo Lipparini
TL;DR
This paper investigates the compactness properties of products of opies of nd or singular and regular cardinals, employing ultrafilters, infinitary languages, and nonstandard analysis to characterize their behavior.
Contribution
It provides a detailed characterization of compactness for products of nd or singular and regular cardinals, extending previous results with new methods.
Findings
Characterization of compactness for nd or singular nd ardinals.
Use of ultrafilters, infinitary languages, and nonstandard elements in the analysis.
Results on products of uncountable regular cardinals with the order topology.
Abstract
We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary languages and nonstandard elements. We also deal with products of uncountable regular cardinals with the order topology.
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