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Indiscernible sequences in a model which fails to have the order property

Published online by Cambridge University Press:  12 March 2014

Rami Grossberg
Rami Grossberg*
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
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Abstract

Basic results on the model theory of substructures of a fixed model are presented. The main point is to avoid the use of the compactness theorem, so this work can easily be applied to the model theory of Lω1,ω and its relatives. Among other things we prove the following theorem:

Let M be a model, and let λ be a cardinal satisfying λ∣L(M)∣ = λ. If M does not have the ω-order property, then for every A ⊆ M, ∣A∣ ≤ λ, and every I ⊆ M of cardinality λ+ there exists J ⊆ I cardinality λ+ which is an indiscernible set over A.

This is an improvement of a result of S. Shelah.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 1 , March 1991 , pp. 115 - 123
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

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