Local order property in nonelementary classes |
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Authors: | Rami Grossberg Olivier Lessmann |
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Institution: | (1) Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA , US |
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Abstract: | Abstract. We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness
theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first
order case. Appropriate localizations of the order property, the independence property, and the strict order property are
introduced. We are able to generalize some of the results that were known in the case of local stability for the first order
theories, and for stability for nonelementary classes (existence of indiscernibles, existence of averages, stability spectrum,
equivalence between order and instability). In the first order case, we also prove the local version of Shelah's Trichotomy
Theorem. Finally, as an application, we give a new characterization of stable types when the ambient first order theory is
simple.
Received: 18 June 1998 |
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Keywords: | |
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