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Turing determinacy and the continuum hypothesis

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Abstract

From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ℵ1 is constructible from a real.

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References

  1. Davis, M.: Infinite games of perfect information. Ann. Math. Stud.52, 85–101 (1964)

    Google Scholar 

  2. Friedman, H.: Determinateness in the low projective hierarchy. Fundam. Math.77, 79–95 (1971)

    Google Scholar 

  3. Friedman, H.: Higher set theory and mathematical practice. Ann. Math. Logic2, 326–357 (1971)

    Google Scholar 

  4. Harrington, L.: Analytic determinacy and 0#. J. Symb. Logic43, 685–693 (1978)

    Google Scholar 

  5. Jech, T.: Set theory. New York: Academic Press 1978

    Google Scholar 

  6. Martin, D.: Measurable cardinals and analytic games. Fundam. Math.66, 287–291 (1970)

    Google Scholar 

  7. Martin, D.: Borel determinacy. Ann. Math. II Ser.102, 363–371 (1975)

    Google Scholar 

  8. Moschovakis, Y.: Descriptive set theory. Amsterdam: North-Holland 1980

    Google Scholar 

  9. Mycielsky, J.: On the axiom of determinateness. Fundam. Math.53, 205–224 (1964)

    Google Scholar 

  10. Sacks, G.: Higher recursion theory. Berlin Heidelberg New York Tokyo: Springer (in press)

  11. Solovay, R.: A model of set theory in which every set is Lebesgue measurable. Ann. Math. II Ser.92, 1–56 (1970)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt

    Ramez L. Sami

  2. U.F.R. de Mathématiques, Université Paris VII, F-75251, Paris Cedex 05, France

    Ramez L. Sami

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  1. Ramez L. Sami
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Sami, R.L. Turing determinacy and the continuum hypothesis. Arch Math Logic 28, 149–154 (1989). https://doi.org/10.1007/BF01622874

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  • DOI: https://doi.org/10.1007/BF01622874

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