Journal of Symbolic Logic

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

Tapani Hyttinen and Olivier Lessmann

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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.

Article information

Source
J. Symbolic Logic, Volume 67, Issue 4 (2002), 1469-1482.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1190150294

Digital Object Identifier
doi:10.2178/jsl/1190150294

Mathematical Reviews number (MathSciNet)
MR1955247

Zentralblatt MATH identifier
1039.03024

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Citation

Hyttinen, Tapani; Lessmann, Olivier. A rank for the class of elementary submodels of a superstable homogeneous model. J. Symbolic Logic 67 (2002), no. 4, 1469--1482. doi:10.2178/jsl/1190150294. https://projecteuclid.org/euclid.jsl/1190150294


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