Self-embeddings of computable trees
Logic
2014-08-12 v1
Abstract
We divide the class of infinite computable trees into three types. For the first and second types, computes a nontrivial self-embedding while for the third type 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 antichain. This result is optimal and has connections to the program of reverse mathematics.
Keywords
Cite
@article{arxiv.1408.2286,
title = {Self-embeddings of computable trees},
author = {Stephen Binns and Bjørn Kjos-Hanssen and Manuel Lerman and James H. Schmerl and Reed Solomon},
journal= {arXiv preprint arXiv:1408.2286},
year = {2014}
}