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On bQ1-degrees of c.e. sets

MATHEMATICAL LOGIC QUARTERLY (2023)

sQ1-degrees of computably enumerable sets

Roland Sh Omanadze

Summary: This article proves that the sQ-degree of a hypersimple set is an infinite collection of degrees linearly ordered under the <=(sQ1) relation, with the order type of the integers, and each c.e. set in these sQ-degrees is a hypersimple set. Additionally, it is proven that there are two c.e. sets that have no least upper bound in the sQ(1)-reducibility ordering. The article also shows that the c.e. sQ(1)-degrees are not dense and provides some properties of a c.e. sQ(1)-degree under certain conditions.

ARCHIVE FOR MATHEMATICAL LOGIC (2023)

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