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- W2968751102 abstract "To determine whether there is a nontrivial automorphism of the Turing degrees remains a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be, and ruled out that an automorphism might be induced by a function on integers. A homeomorphism $F$ of the Cantor space is said to induce a uniform map mod finite if for each $ainomega$ there is a $binomega$ such that for all $X$ and $Y$, if $X(n)=Y(n)$ for all $nge b$ then $F(X)(m)=F(Y)(m)$ for all $mge a$. We show that if such an $F$ induces an automorphism $pi$ of the Turing degrees, then $pi$ is trivial. This generalizes, and provides an easier proof of, the past result where $F$ was assumed to be induced by a permutation of $omega$." @default.
- W2968751102 created "2019-08-22" @default.
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- W2968751102 date "2019-08-15" @default.
- W2968751102 modified "2023-09-27" @default.
- W2968751102 title "On homeomorphisms of Cantor space that induce only the trivial Turing automorphism" @default.
- W2968751102 hasPublicationYear "2019" @default.
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