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The spectrum of resplendency

Published online by Cambridge University Press:  12 March 2014

John T. Baldwin
John T. Baldwin*
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinoisat Chicago, Chicago, Illinois 60680
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Abstract

Let T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 626 - 636
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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