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Forcing minimal degree of constructibility

Published online by Cambridge University Press:  12 March 2014

Haim Judah
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720 Mathematical Sciences Research, Institute Berkeley, California 94720 Department of Mathematics, Bar Ilan University, 52-100 Ramat Gan, Israel Institute of Mathematics, The Hebrew University, Jerusalem, Israel
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Abstract

In this paper we will study four forcing notions, two of them giving a minimal degree of constructibility. These constructions give answers to questions in [Ih].

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1991

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Footnotes

1

Note new spelling (formerly Jaime Ihoda)

References

REFERENCES

[ASh] Abraham, U. and Shore, R., The degrees of constructibility of Cohen reals, Proceedings of the London Mathematical Society, ser. 3, vol. 53 (1986), pp. 193208.CrossRefGoogle Scholar
[Bl] Blass, A., Selective ultrafilters and homogeneity, Annals of Pure and Applied Logic, vol. 38(1988), pp. 215255.CrossRefGoogle Scholar
[BSh] Blass, A. and Shelah, S., There may be simple - and -points and the Rudin-Keisler ordering may be downward directed, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 213243.CrossRefGoogle Scholar
[Gr] Gray, C. W. Iterated forcing from the strategic point of view, Ph.D. thesis, University of California, Berkeley, California, 1980.Google Scholar
[Ih] Ihoda, J., -sets of reals, this Journal, vol. 53 (1988), pp. 636642.Google Scholar
[IShl] Ihoda, J. and Shelah, S., -sets of reals, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 207223.CrossRefGoogle Scholar
[ISh2] Ihoda, J. and Shelah, S., The Kunen-Miller chart, this Journal, vol. 55 (1990), pp. 909927.Google Scholar
[Ma] Mathias, A., Happy families, Annals of Mathematical Logic, vol. 12 (1977), pp. 59111.CrossRefGoogle Scholar
[Mi] Miller, A., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), pp. 93114.CrossRefGoogle Scholar
[Sa] Sacks, G., Forcing with perfect closed sets, Axiomatic set theory (Scott, D., editor), Proceedings of Symposia in Pure Mathematics, vol. 13, part 1, American Mathematical Society, Providence, Rhode Island, 1971, pp. 331355.CrossRefGoogle Scholar