Self-embeddings of computable trees

Stephen Binns; Bjørn Kjos-Hanssen; Manuel Lerman; James H. Schmerl; Reed Solomon

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arXiv · 1408.2286

Self-embeddings of computable trees

Stephen Binns·Bjørn Kjos-Hanssen·Manuel Lerman·James H. Schmerl·Reed Solomon

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Abstract

We divide the class of infinite computable trees into three types. For the first and second types, $0'$ computes a nontrivial self-embedding while for the third type $0''$ computes a nontrivial self-embedding. These results are optimal and we obtain partial results concerning the complexity of nontrivial self-embeddings of infinite computable trees considered up to isomorphism. We show that every infinite computable tree must have either an infinite computable chain or an infinite $\Pi^0_1$ antichain. This result is optimal and has connections to the program of reverse mathematics.

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BibTeX RIS

Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, James H. Schmerl, Reed Solomon. 2014-08-11. Self-embeddings of computable trees. https://arxiv.org/abs/1408.2286

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