Work

Self-embeddings of computable trees

Year: 2014

Type: preprint

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 $Π^0_1$ antichain. This result is optimal and has connections to the program of reverse mathematics.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1408.2286

Authors: Binns, Stephen, Kjos-Hanssen, Bjørn, Lerman, Manuel, Schmerl, James H., Solomon, Reed

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Computability Theory, Reverse Mathematics and Countable Algebraic Structures

OpenAlex ID: W4300722755

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