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FORKING AND SUPERSTABILITY IN TAME AECS

Published online by Cambridge University Press:  09 March 2016

SEBASTIEN VASEY
SEBASTIEN VASEY*
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES CARNEGIE MELLON UNIVERSITY PITTSBURGH, PENNSYLVANIA, USAE-mail: [email protected]: http://math.cmu.edu/∼svasey/
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Abstract

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We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. These methods are applied to obtain an upward stability transfer theorem from categoricity and tameness, as well as new conditions for uniqueness of limit models.

Keywords

Primary: 03C48Secondary: 03C4503C5203C55Abstract elementary classesforkingindependenceclassification theorygood framescategoricitysuperstabilitystabilitystability spectrumtameness
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 357 - 383
Copyright
Copyright © The Association for Symbolic Logic 2016 

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