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On sets of relations definable by addition

Published online by Cambridge University Press:  12 March 2014

James F. Lynch
James F. Lynch*
Affiliation:
Clarkson College of Technology, Potsdam, New York 13676
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Abstract

For every κ ∈ ω, there is an infinite set Aκ ⊆ ω and a d(κ) ∈ ω such that for all Q0, Q1, ⊆ Aκ where ∣Q0∣ = ∣ Q1∣, or d(κ) < ∣Q0∣, Q1∣ < ℵ0, the structures ‹ω, +, Q0› and ‹ω, +, Q1› are indistinguishable by first-order sentences of quantifier depth κ whose atomic formulas are of the form u = v, u + v = w, and Q(u), where u, v, and w are variables.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 3 , September 1982 , pp. 659 - 668
Copyright
Copyright © Association for Symbolic Logic 1982

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References

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