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5 votes
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Splitting 0' into two 1-generic reals

I have come across multiple research papers where they have mentioned that two 1-generic reals $x$ and $y$ can be constructed such that $x \oplus y \equiv_{T} \textbf{0}'$, where $\textbf{0}'$ is the ...
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1 vote
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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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