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The Hanf number of second order logic1

Published online by Cambridge University Press:  12 March 2014

K. Jon Barwise
K. Jon Barwise*
Affiliation:
University of Wisconsin, Madison, Wisconsin 53706
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Abstract

We prove, among other things, that the number mentioned above cannot be shown to exist without using some instance of the axiom of replacement.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 37 , Issue 3 , September 1972 , pp. 588 - 594
Copyright
Copyright © Association for Symbolic Logic 1972

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Footnotes

1

We would like to thank H. J. Keisler and Kenneth Kunen for helpful discussions. The preparation of this paper was supported by NSF grant 144-B634.

References

REFERENCES

[1]Barwise, K. J., Infinitary methods in the model theory of set theory, Logic Colloquium 1969, North-Holland, Amsterdam, 1971, pp. 53–66.Google Scholar
[2]Friedman, H., Set-theoretic problems suggested by rational examination, mimeographed notes, Stanford University, Stanford, California, 1969.Google Scholar
[3]Lévy, A., A hierarchy of formulas in set theory, Memoirs of the American Mathematical Society, No. 57, American Mathematical Society, Providence R.I., 1965.Google Scholar
[4]Skolem, Th., Some remarks on axiomatized set theory, From Frege to Godel, Harvard University Press, Cambridge, Massachusetts, 1967, pp. 290–301.Google Scholar
[5]Zermelo, E., Investigations in the foundations of set theory. I, From Frege to Godel, Harvard University Press, Cambridge, Massachusetts, 1967, pp. 200–215.Google Scholar