Alistair H. Lachlan

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The degrees of unsolvability have been extensively studied by Sacks in (4). This paper studies problems concerned with lower bounds of pairs of recursively enumerable (r.e.) degrees. It grew out of an unpublished paper written in June 1964 which presented a proof of the following conjecture of Sacks ((4) 170): there exist two r.e. degrees a, b whose(More)
Let S denote the lattice of recursively enumerable (r.e.) sets under inclusion, and let #* denote the quotient lattice of S modulo the ideal 3F of finite sets. For A e ê let A* denote the equivalence class in <ƒ* which contains A. An r.e. set A is maximal if A* is a coatom (maximal element) of <f *. Let Aut ê (Aut <f *) denote the group of automorphisms of(More)