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The proper forcing axiom and the singular cardinal hypothesis

  • Matteo Viale (a1) (a2)

Abstract

We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11].

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References

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[1]Caicedo, A. and Veličković, B., Bounded proper forcing axiom and well orderings of the reals, Mathematical Research Letters, to appear, 18 pages.
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[10]Moore, J. T., The proper forcing axiom. Prikry forcing, and the singular cardinals hypothesis, Annals of Pure and Applied Logic, to appear.
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[12]Silver, J. H.. On the singular cardinals problem, Proceedings of the international congress of mathematicians (Vancouver, B. C., 1974), vol. 1, Canadian Mathematical Congress, Montreal. Que., 1975, pp. 265268.
[13]Solovay, R. M., Strongly compact cardinals and the GCH, Proceedings of the Tarski Symposium (Proceedings of the Symposium for Pure Mathematics, Vol. XXV, Univ. California, Berkeley, California, 1971) (Henkin, L.et al., editors), American Mathematical Society, Providence, R.I., 1974, pp. 365372.
[14]Veličković, B.. Forcing axioms and stationary sets, Advances in Mathematics, vol. 94 (1992). no. 2, pp. 256284.
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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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