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Thorn-forking in continuous logic

Published online by Cambridge University Press:  12 March 2014

Clifton Ealy  and
Isaac Goldbring
Clifton Ealy
Affiliation:
Western Illinois University, Department of Mathematics, 476 Morgan Hall, 1 University Circle, Macomb, IL 61455, USA, E-mail: [email protected]
Isaac Goldbring
Affiliation:
University of California, Los Angeles, Department of Mathematics, 520 Portola Plaza, Box 951555, Los Angeles, CA 90095-1555, USA, E-mail: [email protected], URL: www.math.ucla.edu/~isaac
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Abstract

We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for discrete first-order real rosy theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 63 - 93
Copyright
Copyright © Association for Symbolic Logic 2012

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