Automorphisms in the PTIME-Turing degrees of recursive sets

Permutations of the Integers Induce only the Trivial Automorphism of the Turing Degrees

“…Haught and Slaman [2] used permutations of the integers to obtain automorphisms of the polynomial-time Turing degrees in an ideal (below a fixed set).…”

“…Theorem 2 (Haught and Slaman [2]). There is a permutation of 2 <ω , or equivalently of ω, that induces a nontrivial automorphism of (PTIME A , ≤ pT ).…”

Permutations of the Integers Induce Only the Trivial Automorphism of the Turing Degrees

“…[7,19,20] [1,16] [25] [4] Slaman, Woodin 1990 [23] The thought that a permutation of might induce an automorphism of D T might seem frivolous. But Haught and Slaman [9] did use permutations of the integers to obtain automorphisms of the polynomial-time Turing degrees in an ideal (below a fixed set). Theorem 1.3 (Haught and Slaman [9]).…”

“…But Haught and Slaman [9] did use permutations of the integers to obtain automorphisms of the polynomial-time Turing degrees in an ideal (below a fixed set). Theorem 1.3 (Haught and Slaman [9]). There is a permutation of 2 < (equivalently, of ) that induces a nontrivial automorphism of (PTIME A , ≤ pT ) for some A.…”