Relations between table-type degrees (Q790106)

If r is a reducibility, let \(Th(L_ r)\) be the elementary theory of the upper semilattice of the recursively enumerable r-degrees \(L_ r\). It is proved that \((i)\quad Th(L_{tt})\neq Th(L_ p); (ii)\quad Th(L_ l)\neq Th(L_ r)\) for \(r\in \{btt,tt,p,d\}\). An example of a non-recursive btt- degree which contains only one m-degree is also constructed.