Large Cardinal Axioms from Tameness in Aecs
نویسنده
چکیده
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions. For instance, we show: Theorem. Let κ be uncountable such that μω < κ for every μ < κ. If every AEC with Löwenheim-Skolem number less than κ is < κ-tame, then κ is almost strongly compact. This is done by isolating a class of AECs that exhibits tameness, etc. exactly when sufficiently complete ultrafilters exist.
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