Large cardinal axioms from tameness in aecs

Will Boney, Spencer Unger

Research output: Contribution to journalArticlepeer-review


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 that if κ is an uncountable cardinal such that μω <κ for every μ<κ and 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 exactly when sufficiently complete ultrafilters exist.

Original languageEnglish
Pages (from-to)4517-4532
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number10
StatePublished - 2017
Externally publishedYes


Dive into the research topics of 'Large cardinal axioms from tameness in aecs'. Together they form a unique fingerprint.

Cite this