Saturated model

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (January 2010) (Learn how and when to remove this message)

In mathematical logic, and particularly in its subfield model theory, a saturated model M is one that realizes as many complete types as may be "reasonably expected" given its size. For example, an ultrapower model of the hyperreals is ${\displaystyle \aleph _{1}}$-saturated, meaning that every descending nested sequence of internal sets has a nonempty intersection.^[1]