Questions tagged [arithmetic-degree]
Use to describe questions about the structure of the arithmetic degrees (subsets of N under the relation of relative arithmetic definability) as used in higher computability theory.
6 questions with no upvoted or accepted answers
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$\Pi^0_2$ singleton of minimal arithmetic degree?
Is it known if there is a $\Pi^0_2$ singleton of minimal arithmetic degree?
To elaborate a bit, this is asking whether there is a non-arithmetic set $X$ such that for any $Y$ arithmetic in $X$ either ...
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Direct construction of an arithmetically high degree below $0^{(\omega)}$
The existence of a high arithmetic degree (meaning the degrees induced by the notion of relative arithmetic definability) below $0^\omega$ can be established by using Harrington/Simpson's ...
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Is $0^{\omega}$ a minimal cover of a minimal arithmetic degree?
Is there a minimal arithmetic degree $d <_a 0^{\omega}$ such that $0^{\omega}$ is a minimal cover of $d$ in the arithmetic degrees? [1]
While whether or not $0^{\omega}$ is a minimal cover at all (...
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Are the $\omega$-generic arithmetic degrees downward closed
A degree is $\alpha$-generic if it has representative that is $\alpha$-generic. Are the $\omega$-generic arithmetic degrees (i.e. the degree structure induced by arithmetic reproducibility) downward ...
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Base of cone of arithmetic minimal covers
By Borel determinacy (exercisce XIII.1.7 in Odifreddi) there is a cone of minimal covers in the arithmetic degrees. Is the base of such a cone known? A minimal such base?
For that matter, is it even ...
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No arithmetic degree that always joins to arithmetic minimal cover
Is there (I strongly presume not but not seeing how to show it) a (non-zero) arithmetic degree $a$ such that for all arithmetic degrees $e \not\geq_a a$ we have $e \oplus a$ is a minimal cover of $e$ ...
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