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Degrees of models

Published online by Cambridge University Press:  12 March 2014

J. R. Shoenfield
J. R. Shoenfield*
Affiliation:
Duke University
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According to Gödel's completeness theorem, every consistent theory1 has a model whose domain is a set of natural numbers. The objects of the model corresponding to the predicate symbols of the theory are then predicates of natural numbers. Kleene [5] p. 398 showed that, if the theory is axiomatizable,2 then the model can be chosen so that these predicates are in both two-quantifier forms, i.e., they can be expressed in both the forms (x)(Ey)R and (Ex)(y)S with R and S recursive. An alternative proof has been given by Hasen jaeger [3].

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 3 , September 1960, pp. 233 - 237
Copyright
Copyright © Association for Symbolic Logic 1960

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References

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