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Powers of the ideal of Lebesgue measure zero sets

Published online by Cambridge University Press:  12 March 2014

Maxim R. Burke
Maxim R. Burke*
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
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Abstract

We investigate the cofinality of the partial order κ of functions from a regular cardinal κ into the ideal of Lebesgue measure zero subsets of R. We show that when add () = κ and the covering lemma holds with respect to an inner model of GCH, then cf (κ) = max{cf(κκ), cf([cf()]κ)}. We also give an example to show that the covering assumption cannot be removed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 1 , March 1991 , pp. 103 - 107
Copyright
Copyright © Association for Symbolic Logic 1991

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References

REFERENCES

[Baum]Baumgartner, J. E., Iterated forcing, Surveys in set theory (Mathias, A. R. D., editor), Cambridge University Press, Cambridge, 1983, pp. 1–59.Google Scholar
[Burke]Burke, M. R., Some applications of set theory to measure theory, Ph.D. thesis, University of Toronto, Toronto, 1988.Google Scholar
[Frem 1]Fremlin, D. H., On the additivity and cofinality of Radon measures, Mathematika, vol. 31 (1984), pp. 323–335.CrossRefGoogle Scholar
[Frem 2]Fremlin, D. H., Cichon's diagram, Séminaire d'Initiation à l'Analyse (Choquet, G.et al., editors), vol. 23, Université Pierre et Marie Curie, Paris, 1984, pp. 5.01–5.13.Google Scholar
[Frem 3]Fremlin, D. H., The partially ordered sets of measure theory and Tukey's ordering, preprint, 1988.Google Scholar
[Jech]Jech, T., Set theory, Academic Press, New York, 1973.Google Scholar
[Kun]Kunen, K., Random and Cohen reals, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 887–911.CrossRefGoogle Scholar
[Mag]Magidor, M., On the singular cardinals problem. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 1–31.CrossRefGoogle Scholar