Minimal degrees which are Σ₂⁰ but not Δ₂⁰

Author:

Shore Richard

Abstract

We give a short proof of the existence of minimal Turing degrees which are Σ 2 0 \Sigma _{2}^{0} but not Δ 2 0 \Delta _{2}^{0} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference11 articles.

1. One hundred and two problems in mathematical logic;Friedman, Harvey;J. Symbolic Logic,1975

2. Recursiveness in 𝑃¹₁ paths through \cal𝑂;Friedman, Harvey;Proc. Amer. Math. Soc.,1976

3. Goncharov, S. S., Harizanov, V. S., Knight, J. and Shore, R. A., Π₁¹ relations and paths through 𝒪, in preparation.

4. Recursiveness of initial segments of Kleene’s 𝑂;Jockusch, Carl G., Jr.;Fund. Math.,1975

5. Π⁰₁ classes and degrees of theories;Jockusch, Carl G., Jr.;Trans. Amer. Math. Soc.,1972

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