Hyperhypersimple sets and Q1 -reducibility
Irakli O. Chitaia · Mathematical logic quarterly · 2016
We prove that the c.e. Q1-degrees are not dense, and there exists a c.e. Q1-degree with no minimal c.e. predecessors. It is proved that if M1 and M2 are maximal sets such that then or . We also show that there exist infinite collections of Q1-degrees and such that the following hold: (i) for every , , , and , (ii) each consists entirely of maximal sets; and (iii) each consists entirely of non-maximal hyperhypersimple sets.