By Cantor's intersection theorem every decreasing nested sequence of nonempty compact sets has a common point. A superficially similar result holds that every decreasing nested sequence of nonempty internal sets in the hyperreals ${}^\ast\mathbb{R}$ has a common point, a property known as countable saturation. Is such a resemblance more than superficial?
How is compactness related to countable saturation?
Mikhail Katz
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