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An inner model for global domination

  • Sy-David Friedman (a1) and Katherine Thompson (a2)

Abstract

In this paper it is shown that the global statement that the dominating number for κ is less than 2κ for all regular κ, is internally consistent, given the existence of 0#. The possible range of values for the dominating number for κ and 2κ which may be simultaneously true in an inner model is also explored.

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[1]Cummings, J. and Shelah, S., Cardinal invariants above the continuum. Annals of Pure and Applied Logic, vol. 75 (1995), pp. 251268.
[2]Dobrinen, N. and Friedman, S., The tree property at the double successor of a measurable, submitted.
[3]Džamonja, M., Friedman, S., and Thompson., K., Global complexity results, Set theory: Recent trends and applications (Andretta, A., editor), Quaderni di Matematica, vol. 17, Seconda Universita di Napoli, 2007, pp. 2545.
[4]Friedman, S. and Ondrejović, P., Internal consistency of Easton's theorem, Annals of Pure and Applied Logic, to appear.
[5]Friedman, S. and Thompson, K., Internal consistency for embedding complexity, this Journal, vol. 73 (2008), no. 3, pp. 831844.
[6]Friedman, S. and Thompson, K., Perfect trees and elementary embeddings, this Journal, vol. 73 (2008), no. 3, pp. 906918.
[7]Kanamori, A., Perfect-set forcing for uncountable cardinals, Annals of Mathematical Logic, vol. 19 (1980), pp. 97114.
[8]Kanamori, A., The higher infinite, Perspectives in Mathematical Logic, Springer-Verlag, 1997.
[9]Mekler, A. and Väänänen, J., Trees and -subsets of, this Journal, vol. 58 (1993), no. 3, pp. 10521070.

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An inner model for global domination

  • Sy-David Friedman (a1) and Katherine Thompson (a2)

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