Permutations of the integers induce only the trivial automorphism of the Turing degrees

Bjørn Kjos-Hanssen

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arXiv · 1603.00525

Permutations of the integers induce only the trivial automorphism of the Turing degrees

Bjørn Kjos-Hanssen

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Abstract

Let $\pi$ be an automorphism of the Turing degrees induces by a homeomorphism $\varphi$ of the Cantor space $2^\omega$ such that $\varphi$ preserves all Bernoulli measures. It is proved that $\pi$ must be trivial. In particular, a permutation of $\omega$ can only induce the trivial automorphism of the Turing degrees.

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BibTeX RIS

Bjørn Kjos-Hanssen. 2016-03-02. Permutations of the integers induce only the trivial automorphism of the Turing degrees. https://arxiv.org/abs/1603.00525

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