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The extended plus-one hypothesis—A relative consistency result

Published online by Cambridge University Press:  22 January 2016

Theodore A. Slaman
Theodore A. Slaman*
Affiliation:
Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, Illinois 60687USA
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This paper includes a proof, relative to the consistency of ZFC, of the consistency of ZFC, the continuum has singular cardinality and the extended plus-one hypothesis.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 92 , December 1983 , pp. 107 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Gandy, R. O., Generalized recursive functionals of finite type, paper given at the symposium on mathematical logic held at University of Clermont Ferrand (1962).Google Scholar
[2] Griffor, E. R. and Normann, D., Effective cofinalities and admissibility in E-recursion, University of Oslo, preprint (1982).Google Scholar
[3] Grilliot, T. J., Selection functions for recursive functionals, Notre Dame. J. Formal Logic, 10 (1969), 225–234.CrossRefGoogle Scholar
[4] Harrington, L. A. and MacQueen, D. B., Selection in abstract recursion theory, J. Symbolic Logic, 41 (1976), 153–158.Google Scholar
[5] Harrington, L. A., Contributions to recursion theory on higher types, Ph.D. Thesis, M.I.T., Cambridge, MA, (1973).Google Scholar
[6] Harrington, L. A., Long projective well orderings, Ann. of Math. Logic, 12 (1977), 1–24.CrossRefGoogle Scholar
[7] Jech, T., Set Theory, Academic Press, New York, 1978.Google Scholar
[8] Kleene, S. C., Recursive functionals and quantifiers of finite types I and II, Trans. Amer. Math. Soc., 91 and 108 (1959 and 1963), 1–52 and 106–142.Google Scholar
[9] Moschovakis, Y. N., Hyperanalytic predicates, Trans. Amer. Math. Soc., 138 (1967), 249–282.CrossRefGoogle Scholar
[10] Normann, D., Set recursion in: Generalized Recursion Theory II, North Holland, Amsterdam, 1978.CrossRefGoogle Scholar
[11] Sacks, G. E., The k-section of a type n object, Amer. J. Math., 99 (1977), 901–917.Google Scholar
[12] Sacks, G. E., Three aspects of recursive enumerability, in: Drake, F. R. and Wainer, S. S. eds, Recursion Theory : its Generalisations and Applications, Cambridge University Press, Cambridge, 1979.Google Scholar
[13] Sacks, G. E., On the limits of recursive enumerability, to appear.Google Scholar
[14] Sacks, G. E., Post’s problem in E-recursion, to appear.Google Scholar
[15] Sacks, G. E., Selection and forcing, to appear.Google Scholar
[16] Sacks, G. E. and Slaman, T. A., Inadmissible forcing, to appear.Google Scholar
[17] Slaman, T. A., Aspects of E-recursion, Ph.D. Thesis, Harvard University, Cambridge, MA, (1981).Google Scholar