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Mikhail Katz
Mikhail Katz
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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 hyperrealsan ultrapower model of a hyperreal field ${}^\ast\mathbb{R}$ has a common point, a property known as countable saturation. 

Is such a resemblance more than superficial?

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?

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 an ultrapower model of a hyperreal field ${}^\ast\mathbb{R}$ has a common point, a property known as countable saturation. 

Is such a resemblance more than superficial?

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Mikhail Katz
Mikhail Katz
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How is compactness related to countable saturation?

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?