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Diverse classes

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 Illinois at Chicago, Chicago, Illinois 60680
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Abstract

Let I(μ, Κ) denote the number of nonisomorphic models of power μ and IE(μ, Κ) the number of nonmutually embeddable models. We define in this paper the notion of a diverse class and use it to prove a number of results. The major result is Theorem B: For any diverse class Κ and μ greater than the cardinality of the language of Κ,

From it we deduce both an old result of Shelah, Theorem C: If T is countable and λ0 > ℵ0 then for every μ > ℵ0, IE(μ, T) ≥ min(2μ, ⊐2), and an extension of that result to uncountable languages, Theorem D: If ∣T∣ < 2ωλ0 > ∣T∣, and ∣D(T)∣ = ∣T∣ then for μ > ∣T∣,

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 875 - 893
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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