Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A basis result for $ \Sigma \sp{0}\sb{3}$ sets of reals with an application to minimal covers

Authors: Leo A. Harrington and Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 53 (1975), 445-448
MSC: Primary 02K30; Secondary 02F30, 04A15
MathSciNet review: 0398832
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every $ \Sigma _3^0$ set of reals which contains reals of arbitrarily high Turing degree in the hyperarithmetic hierarchy contains reals of every Turing degree above the degree of Kleene's $ \mathcal{O}$. As an application it is shown that every Turing degree above the Turing degree of Kleene's $ \mathcal{O}$ is a minimal cover.

References [Enhancements On Off] (What's this?)

  • [1] C. G. Jockusch, Jr., An application of $ \sum _4^0$ determinacy to the degrees of unsolvability, J. Symbolic Logic 38 (1973), 293-294. MR 0332459 (48:10786)
  • [2] D. A. Martin, Two theorems on Turing determinacy, Mimeographed notes, June 1974.
  • [3] -, The axiom of determinateness and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74 (1968), 687-689. MR 37 #2607. MR 0227022 (37:2607)
  • [4] Y. N. Moschovakis, Elementary induction in abstract structures, North-Holland, Amsterdam, 1974.
  • [5] H. Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967. MR 37 #61. MR 0224462 (37:61)
  • [6] G. E. Sacks, Degrees of unsolvability, Ann. of Math. Studies, no. 55, Princeton Univ. Press, Princeton, N. J., 1963. MR 32 #4013. MR 0186554 (32:4013)
  • [7] J. R. Shoenfield, Mathematical logic, Addison-Wesley, Reading, Mass., 1967. MR 37 #1224. MR 0225631 (37:1224)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02K30, 02F30, 04A15

Retrieve articles in all journals with MSC: 02K30, 02F30, 04A15

Additional Information

Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society