Large cardinal axioms from tameness in AECs
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- by Will Boney and Spencer Unger PDF
- Proc. Amer. Math. Soc. 145 (2017), 4517-4532 Request permission
Abstract:
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 $\kappa$ is an uncountable cardinal such that $\mu ^\omega < \kappa$ for every $\mu < \kappa$ and every AEC with Löwenheim-Skolem number less than $\kappa$ is $<\kappa$-tame, then $\kappa$ is almost strongly compact. This is done by isolating a class of AECs that exhibits tameness exactly when sufficiently complete ultrafilters exist.References
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Additional Information
- Will Boney
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- MR Author ID: 1094293
- Email: wboney@math.harvard.edu
- Spencer Unger
- Affiliation: Department of Mathematics, University of California-Los Angeles, Los Angeles, California 90095
- MR Author ID: 983745
- Email: sunger@math.ucla.edu
- Received by editor(s): October 6, 2015
- Received by editor(s) in revised form: July 5, 2016, October 7, 2016, and October 19, 2016
- Published electronically: April 7, 2017
- Communicated by: Mirna Džamonja
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4517-4532
- MSC (2010): Primary 03C45, 03E55, 03C48
- DOI: https://doi.org/10.1090/proc/13555
- MathSciNet review: 3690634