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A rank for the class of elementary submodels of a superstable homogeneous model

Published online by Cambridge University Press:  12 March 2014

Tapani Hyttinen  and
Olivier Lessmann
Tapani Hyttinen
Affiliation:
Department of Mathematics, University of Helsinki, P.O. Box 4, 00014, Finland, E-mail: tapani.hyttinen@helsinki.fi
Olivier Lessmann
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK, E-mail: lessmann@maths.ox.ac.uk
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Abstract

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence relation for superstable homogeneous models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1469 - 1482
Copyright
Copyright © Association for Symbolic Logic 2002

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