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Stationary subsets of [ℵω]<ωn

Published online by Cambridge University Press:  12 March 2014

Kecheng Liu
Kecheng Liu*
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717
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Abstract

In this paper, assuming large cardinals, we prove the consistency of the following:

Let n ∈ ω and k1, k2 ≤ n. Let f: ω → {k1, k2} be such that for all n1 < n2 ∈ f−1{k1},n2 − n1 ≥ 4. Then the set

is stationary in

The above is equivalent to the statement that for any structure on on ℵω, there is ≺ A such that ∣∣ = ωn and for all m > n, cf( ∩ ωm) = ωf(m).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1201 - 1218
Copyright
Copyright © Association for Symbolic Logic 1993

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References

REFERENCES

[1]Baumgartner, J., On the size of closed unbounded sets, manuscript.Google Scholar
[2]Baumgartner, J., Iterated forcing, Surveys in set theory, Cambridge University Press, London and New York, 1983, pp. 1–59.Google Scholar
[3]Foreman, M., More saturated ideals, Lecture Notes in Mathematics, vol. 1019, Springer-Verlag, Berlin, New York, and Heidelberg, 1983.Google Scholar
[4]Foreman, M., Large cardinals and strong model theoretic transfer properties, Transactions of the American Mathematical Society, vol. 272 (1982), pp. 427–463.CrossRefGoogle Scholar
[5]Kanamori, A. and Magidor, M., The evolution of large cardinal axioms in set theory. Higher set theory, Lecture Notes in Mathematics, vol. 669, Springer-Verlag, Berlin, New York, and Heidelberg, 1978.CrossRefGoogle Scholar
[6]Kunen, K., Saturated ideals, this Journal, vol. 43 (1978), pp. 65–76.Google Scholar
[7]Kunen, K., Set theory. An introduction to independence proofs, North-Holland, Amsterdam, 1980.Google Scholar
[8]Laver, R., An (ℵ2, ℵ2, ℵ0)-saturated ideal on ω, Logic colloquium 1980 (Prague), North-Holland, Amsterdam, 1982.Google Scholar
[9]Martin, D., Infinite games, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), ICM, 1980, pp. 269–273.Google Scholar