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Natural models of ackermann's set theory

Published online by Cambridge University Press:  12 March 2014

Rudolf Grewe
Rudolf Grewe*
Affiliation:
University of Illinois at Chicago Circle
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Extract

In 1956 W. Ackermann proposed a new axiomatic set theory, that has received some attention in recent years. (See references [3], [4], [6], [7], and [9].) This theory distinguishes between sets and classes. In this paper we study mainly the natural models of this theory. We show, among other results, that the set-theoretical fragment of these models are also models of Zermelo-Fraenkel set theory. This result gives a partial answer to the question, raised by A. Levy, of the relative strength of Ackermann's set theory with respect of Zermelo-Fraenkel's.2

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 481 - 488
Copyright
Copyright © Association for Symbolic Logic 1969

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References

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