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Gregory trees, the continuum, and Martin's axiom

Published online by Cambridge University Press:  12 March 2014

Kenneth Kunen  and
Dilip Raghavan
Kenneth Kunen
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wi 53706, USA, E-mail: [email protected], URL: http://www.math.wisc.edu/~kunen, E-mail: [email protected], URL: http://www.math.wisc.edu/~raghavan
Dilip Raghavan
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wi 53706, USA, E-mail: [email protected], URL: http://www.math.wisc.edu/~kunen, E-mail: [email protected], URL: http://www.math.wisc.edu/~raghavan
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Abstract

We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.

Keywords

Martin's axiomGregory treeproper forcing03E35
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 712 - 720
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[1]Gregory, J., A countably distributive complete Boolean algebra not uncountably representable, Proceedings of the American Mathematical Society, vol. 42 (1974), pp. 42–46.CrossRefGoogle Scholar
[2]Gregory, J., Higher Souslin trees and the generalized continuum hypothesis, this Journal, vol. 41 (1976), pp. 663–671.Google Scholar
[3]Hart, J. and Kunen, K., Inverse limits and function algebras, Topology Proceedings, vol. 30 (2006), pp. 501–521.Google Scholar
[4]Hart, J. and Kunen, K., First countable continua and proper forcing, Canadian Journal of Mathematics, to appear.Google Scholar
[5]Kunen, K., Set theory, North-Holland, 1980.Google Scholar
[6]Moore, J. T., Hrušák, M., and Džamonja, M., Parametrized ⟡ principles, Transactions of the American Mathematical Society, vol. 356 (2004), pp. 2281–2306.CrossRefGoogle Scholar