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A completeness theorem for Zermelo-Fraenkel set theory

Published online by Cambridge University Press:  12 March 2014

William C. Powell
William C. Powell*
Affiliation:
Katholieke Universiteit, Numegen, Holland
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Extract

We provide a semantics for Zermelo-Fraenkel set theory. The semantics was essentially given by W. Ackermann [1], and the proof of completeness follows from a lemma of Levy [4]. Furthermore, a close relationship between Ackermann's set theory and Zermelo-Fraenkel set theory has been established by Levy [4] and Reinhardt [6]. Thus, any interest in this paper must consist solely in the explicit formulation of the completeness result and the consequential evidence of the fundamental character of Ackermann's principle and the ad hoc character of the full law of excluded middle and the strong transitivity of Ackermann's unary relation

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 2 , June 1976 , pp. 323 - 327
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Ackermann, W., Zur Axiomatik der Mengenlehre, Mathematische Annalen, vol. 131 (1956), pp. 336–345.CrossRefGoogle Scholar
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