Citations of:
Some properties of r-maximal sets and Q 1,N -reducibility
Archive for Mathematical Logic 54 (7-8):941-959 (2015)
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We show that the sQ-degree of a hypersimple set includes an infinite collection of $$sQ_1$$ -degrees linearly ordered under $$\le _{sQ_1}$$ with order type of the integers and each c.e. set in these sQ-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the $$sQ_1$$ -reducibility ordering. We show that the c.e. $$sQ_1$$ -degrees are not dense and if a is a c.e. $$sQ_1$$ -degree such that $$o_{sQ_1}<_{sQ_1}a<_{sQ_1}o'_{sQ_1}$$, then there exist (...) No categories |
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We show that the sQ-degree of a hypersimple set includes an infinite collection of \-degrees linearly ordered under \ with order type of the integers and each c.e. set in these sQ-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the \-reducibility ordering. We show that the c.e. \-degrees are not dense and if a is a c.e. \-degree such that \, then there exist infinitely many pairwise sQ-incomputable c.e. (...) No categories |