A basis result for $\Sigma ^{0}_{3}$ sets of reals with an application to minimal covers
HTML articles powered by AMS MathViewer
- by Leo A. Harrington and Alexander S. Kechris PDF
- Proc. Amer. Math. Soc. 53 (1975), 445-448 Request permission
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
- Carl G. Jockusch Jr., An application of $\sum ^{0}_{4}$ determinacy to the degrees of unsolvability, J. Symbolic Logic 38 (1973), 293–294. MR 332459, DOI 10.2307/2272064 D. A. Martin, Two theorems on Turing determinacy, Mimeographed notes, June 1974.
- Donald A. Martin, The axiom of determinateness and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74 (1968), 687–689. MR 227022, DOI 10.1090/S0002-9904-1968-11995-0 Y. N. Moschovakis, Elementary induction in abstract structures, North-Holland, Amsterdam, 1974.
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
- Gerald E. Sacks, Degrees of unsolvability, Princeton University Press, Princeton, N.J., 1963. MR 0186554
- Joseph R. Shoenfield, Mathematical logic, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967. MR 0225631
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 445-448
- MSC: Primary 02K30; Secondary 02F30, 04A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0398832-7
- MathSciNet review: 0398832