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ℵ0-Complete cardinals and transcendency of cardinals

Published online by Cambridge University Press:  12 March 2014

Kanji Namba
Kanji Namba*
Affiliation:
Tokyo University of Education
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Extract

In this paper, we shall state some results concerning ℵ0-complete cardinals and the transcendency of cardinals which is proposed by G. Takeuti [6]. The main purpose of this paper is to prove the following theorems.

Theorem 1. Let ℵ1, be the first ℵ0-complete cardinal number. Then the transcendency of cardinals holds for Δ11-functions of ℵ1-language.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 4 , February 1968 , pp. 452 - 472
Copyright
Copyright © Association for Symbolic Logic 1968

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References

REFERENCES

[1]Kochen, S., Ultraproducts in the theory of models, Annals of mathematics, vol. 74 (1961), pp. 221–261.CrossRefGoogle Scholar
[2]Kreisel, G., The axiom of choice and the class of hyperarithmetical functions, Indagationes Mathematicae, vol. 24 (1962), pp. 307–391.CrossRefGoogle Scholar
[3]Namba, K., On ℵ0-complete cardinals, Journal of the Mathematical Society of Japan, to appear.Google Scholar
[4]Scott, D., Measurable cardinals and constructible sets, Bulletin de l'Academie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 9 (1961), pp. 521–524.Google Scholar
[5]Takeuti, G., On the recursive functions of ordinal numbers, Journal of the Mathematical Society of Japan, vol. 12 (1960), pp. 119–127.CrossRefGoogle Scholar
[6]Takeuti, G., Transcendency of cardinals, this Journal, vol. 30 (1965), pp. 1–7.Google Scholar