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A method of modelling the formalism of set theory in axiomatic set theory1

Published online by Cambridge University Press:  12 March 2014

A. H. Kruse
A. H. Kruse*
Affiliation:
New Mexico State University, University Park, N.M.
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Extract

As is well known, some paradoxes arise through inadequate analysis of the meanings of terms in a language, an adequate analysis showing that the paradoxes arise through a lack of separation of an object theory and a metatheory. Under such an adequate analysis in which parts of the metatheory are modelled in the object theory, the paradoxes give way to remarkable theorems establishing limitations of the object theory.

Such a modelling is often accomplished by a Gödel numbering. Here we shall use a somewhat different technique in axiomatic set theory, from which we shall reap a few results having the effect of comparing the strength of various axiom schema of comprehension for sets and classes (cf. the numbered results of §§5–7). Similar results were obtained by A. Mostowski [7] using Gödel numbering (cf. 5.3 and 7.3 below).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 1 , March 1963 , pp. 20 - 34
Copyright
Copyright © Association for Symbolic Logic 1964

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Footnotes

1

The writer expresses thanks to the referee for several comments which have helped to round out this paper.

References

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