Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-23T22:27:30.118Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Ackermann, W., Zur Axiomatik der Mengenlehre, Mathemathehe Annalen, vol. 131 (1956), pp. 336–345.CrossRefGoogle Scholar
[2]Grewe, R., On Ackermann's set theory, Ph.D. dissertation, University of California, Los Angeles, 1966.Google Scholar
[3]Lévy, A., On Ackermann's set theory, this Journal, vol. 24 (1959), pp. 154–166.Google Scholar
[4]Lévy, A. and Vaught, R. L., Principles of partial reflexion in the set theories of Zermelo and Ackermann, Pacific journal of mathematics, vol. 11 (1961), pp. 1045–1062.CrossRefGoogle Scholar
[5]Montague, R. and Vaught, R. L., Natural models of set theory, Fundamenta mathematicae, vol. 47 (1959), pp. 219–242.CrossRefGoogle Scholar
[6]Reinhardt, W. N., Ackermann's set theory coincides with ZF, Notices of the American Mathematical Society, vol. 13 (1966), p. 727.Google Scholar
[7]Scott, D., Review of “Zur Axiomatik der Mengenlehre”, by Wilhelm Ackermann, this Journal, vol. 23 (1958), pp. 215–216.Google Scholar
[8]Tarski, A. and Vaught, R. L., Arithmetical extensions of relational systems, Compositio mathematica, vol. 13 (1957), pp. 81–102.Google Scholar
[9]Wang, H., A survey of mathematical logic, Studies in logic and the foundations of mathematics, North-Holland, Amsterdam, 1963.Google Scholar