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Small forcings and Cohen reals

Published online by Cambridge University Press:  12 March 2014

Jindřich Zapletal
Jindřich Zapletal*
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA. E-mail: [email protected]
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Abstract

We show that all posets of uniform density ℵ1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of result.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 280 - 284
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1]Davies, P. C., Small Baire spaces and σ-dense partial orders, Ph.D. thesis, University of Toronto, 1979.Google Scholar
[2]Foreman, M., Magidor, M., and Shelah, S., Martin's maximum, saturated ideals, and non-regular ultrafilters, Part I, Annals of Mathematics, vol. 127 (1988), pp. 1–47.CrossRefGoogle Scholar
[3]Jech, T., Set Theory, Academic Press, New York, 1978.Google Scholar
[4]Judah, H. and Rosłanowski, A., Martin axiom and the continuum, preprint, 1994.Google Scholar
[5]Kunen, K., Small Baire spaces, handwritten notes, 1979.Google Scholar
[6]Rosłanowski, A. and Shelah, S., Simple forcing notions and forcing axioms, preprint, 1994.Google Scholar
[7]Shelah, S., Proper forcing, Lecture Notes in Mathematics, no. 940, Springer-Verlag, Berlin, 1981.Google Scholar
[8]Shelah, S. and Todorcevic, S., A note on small Baire spaces, Canadian Journal of Mathematics, vol. 63 (1986), pp. 659–665.CrossRefGoogle Scholar
[9]Stanley, M. C., Forcing disabled, this Journal, vol. 57 (1992), pp. 1153–1175.Google Scholar
[10]Todorcevic, S., Some consequences of MA +¬wKH, Topology Appl., vol. 12 (1981),pp. 187–208.CrossRefGoogle Scholar
[11]Todorcevic, S., Some combinatorial properties of trees, Bulletin of the London Mathematical Society, vol. 14 (1982), pp. 213–217.CrossRefGoogle Scholar