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The independence property in generalized dense pairs of structures

Published online by Cambridge University Press:  12 March 2014

Alexander Berenstein ,
Alf Dolich  and
Alf Onshuus
Alexander Berenstein
Affiliation:
Universidad de Los Andes, CRA 1 NO 18A-10, Bogotá, Colombia, E-mail: aberenst@uniandes.edu.co, URL: www.matematicas.uniandes.edu.co/~aberenst
Alf Dolich
Affiliation:
East Stroudsburg University, 200 Prospect St. East Stroudsburg, Pennsylvania 18301, USA, E-mail: adolich@po-box.esu.edu, URL: www.dolich.com
Alf Onshuus
Affiliation:
Universidad de Los Andes, CRA 1 NO 18A-10, Bogotá, Colombia, E-mail: aonshuus@uniandes.edu.co
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Abstract

We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.

Keywords

Rosy theorieslovely pairsdense pairsdependent theoriesstrongly dependent theories
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 391 - 404
Copyright
Copyright © Association for Symbolic Logic 2011

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