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On definability of ordinals in logic with infinitely long expressions1

Published online by Cambridge University Press:  12 March 2014

Akiko Kino
Akiko Kino*
Affiliation:
Hughes Aircraft Company, Fullerton, California
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Extract

Let Ω be an infinite cardinal larger than ω. By Lω we mean a language with infinitely long expressions having no individual constants, and such that the only predicates are < and =, and the length of ν or ∃ in a formula in Lω is smaller than Ω (cf. §2).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 365 - 375
Copyright
Copyright © Association for Symbolic Logic 1996

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Footnotes

1

This work was done at Hughes Aircraft Company, Fullerton, California, and was sponsored by the Air Force Systems Command, Research and Technology Division, Rome Air Development Center, Griffiss Air Force Base, New York, 13442, under contract AF30(602)-3339. The author wishes to express her heart-felt thanks to Professor G. Takeuti for his valuable advice during the preparation of this paper. She is also indebted to Mr. G. E. Cash, Drs. F. B. Cannonito and V. H. Dyson for reading this paper in manuscript and correcting her English, and to the referee for his kind suggestions.

References

[1]Bachmann, H., Transfinite Zahlen, Springer, 1955.CrossRefGoogle Scholar
[2]Feferman, S., Some recent work of Ehrenfeucht and Fraïssé, Summaries of talks presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, pp. 201–209.Google Scholar
[3]Takeuti, G., A metamathematical theorem on the theory of ordinal numbers, Journal of the Mathematical Society of Japan, vol. 4 (1952), pp. 146–165.CrossRefGoogle Scholar
[4]Takeuti, G. and Kino, A., On predicates with constructive infinitely long expressions, Journal of the Mathematical Society of Japan, vol. 15 (1963), pp. 176–190.CrossRefGoogle Scholar
[5]Tarski, A., Some problems and results relevant to the foundations of set theory, Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Stanford, 1962, pp. 125–135.Google Scholar