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Gregory trees, the continuum, and Martin's axiom

  • Kenneth Kunen (a1) and Dilip Raghavan (a1)

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.

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References

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[1]Gregory, J., A countably distributive complete Boolean algebra not uncountably representable, Proceedings of the American Mathematical Society, vol. 42 (1974), pp. 4246.
[2]Gregory, J., Higher Souslin trees and the generalized continuum hypothesis, this Journal, vol. 41 (1976), pp. 663671.
[3]Hart, J. and Kunen, K., Inverse limits and function algebras, Topology Proceedings, vol. 30 (2006), pp. 501521.
[4]Hart, J. and Kunen, K., First countable continua and proper forcing, Canadian Journal of Mathematics, to appear.
[5]Kunen, K., Set theory, North-Holland, 1980.
[6]Moore, J. T., Hrušák, M., and Džamonja, M., Parametrized ⟡ principles, Transactions of the American Mathematical Society, vol. 356 (2004), pp. 22812306.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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