论文信息 - Self-Embeddings of Computable Trees

Self-Embeddings of Computable Trees

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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