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The relative consistency of g < cf(Sym(ω))

Published online by Cambridge University Press:  12 March 2014

Heike Mildenbergert*
Affiliation:
The Hebrew University of Jerusalem, Institute of Mathematics, Givat Ram. 91904 Jerusalem., Israel, E-mail: [email protected]
*
Universität Wien. Institut für Formale Logik. Währinger Str. 25, A-1090, Vienna, Austria, E-mail: [email protected]

Abstract

We prove the consistency result from the title. By forcing we construct a model of g = ℵ1, b = cf(Sym(ω)) = ℵ2.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Abraham, U.Proper Forcing, Handbook of Set Theory (Foreman, M., Kanamori, A., and Magidor, M., editors), Kluwer, to appear.Google Scholar
[2]Abraham, U., Shelah, S., and Solovay, R., Squared diamonds, Fundamenta Mathematicae, vol. 78 (1982), pp. 165181.Google Scholar
[3]Devlin, K., Constructibility, Omega Series, Springer, 1980.Google Scholar
[4]Kunen, K., Set Theory, An Introduction to Independence Proofs, North-Holland, 1980.Google Scholar
[5]Mathias, A., Happy families, Annals of Mathematical Logic, vol. 12 (1977), pp. 59111.CrossRefGoogle Scholar
[6]Shelah, S., Non-elementary proper forcing notions, Journal of Applied Analysis, submitted.Google Scholar
[7]Shelah, S., Proper and Improper Forcing, Springer, 1977.Google Scholar
[8]Shelah, S., Tree forcings, preprint, 2000.Google Scholar
[9]Thomas, S., Groupwise density and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 37 (1998), pp. 483493.CrossRefGoogle Scholar