Full Idea
A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal.
Gist of Idea
Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 6.5)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.158
A Reaction
This means you can't have a countable model to represent a fact about infinite sets.
Related Idea
Idea 13658 Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro]