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Encoding orders and trees in binary relations

Part of: Model theory

Published online by Cambridge University Press:  26 February 2010

Wilfrid Hodges
Wilfrid Hodges
Affiliation:
Department of Mathematics, Bedford College, Regent's Park, London NW1 4NS.
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Extract

In Section 1 below I describe two measures of the complexity of a binary relation. J The theorem says that these two measures never disagree very much. Both measures of complexity arose in connection with Saharon Shelah's notion [5] of a stable firstt order theory; Shelah showed in effect that one measure is finite, if, and only if, the other is finite too. This follows trivially from the theorem below. I confess my main aim was not to get the extra information which the theorem provides, but to eliminate Shelah's use of uncountable cardinals, which seemed strangely heavy machinery for proving a purely finitary result. Section 2 below explains the modeltheoretic setting.

MSC classification

Secondary: 03C05: Equational classes, universal algebra

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Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 67 - 71
Copyright
Copyright © University College London 1981

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References

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5.Shelah, S.. Classification theory (North-Holland, Amsterdam 1978).Google Scholar