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Shelah's categoricity conjecture from a successor for tame abstract elementary classes

Published online by Cambridge University Press:  12 March 2014

Rami Grossberg  and
Monica Vandieren
Rami Grossberg
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh
Monica Vandieren
Affiliation:
Department of Mathematics, University of Michigan
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Abstract

We prove a categoricity transfer theorem for tame abstract elementary classes.

Suppose that K is a χ-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let λ ≥ Max{χ, LS(K+}. If K is categorical in λ and λ+, then K is categorical in λ++.

Combining this theorem with some results from [37]. we derive a form of Shelah's Categoricity Conjecture for tame abstract elementary classes:

Suppose K is χ-tame abstract elementary class satisfying the amalgamation and joint embedding properties. Let μ0 ≔ Hanf(K). Ifand K is categorical in somethen K is categorical in μ for all μ .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 553 - 568
Copyright
Copyright © Association for Symbolic Logic 2006

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