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TAMENESS AND FRAMES REVISITED

Published online by Cambridge University Press:  08 September 2017

WILL BONEY  and
SEBASTIEN VASEY
WILL BONEY
Affiliation:
MATHEMATICS DEPARTMENT HARVARD UNIVERSITY CAMBRIDGE, MA 02138, USA E-mail: wboney@math.harvard.edu URL: http://math.harvard.edu/∼wboney/
SEBASTIEN VASEY
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213, USA E-mail: sebv@cmu.edu URL: http://math.cmu.edu/∼svasey/
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Abstract

We study the problem of extending an abstract independence notion for types of singletons (what Shelah calls a good frame) to longer types. Working in the framework of tame abstract elementary classes, we show that good frames can always be extended to types of independent sequences. As an application, we show that tameness and a good frame imply Shelah’s notion of dimension is well-behaved, complementing previous work of Jarden and Sitton. We also improve a result of the first author on extending a frame to larger models.

Keywords

Primary 03C48Secondary 03C4703C5203C55abstract elementary classesgood framessymmetry

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 995 - 1021
Copyright
Copyright © The Association for Symbolic Logic 2017 

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