Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 49, Number 1 (2008), 1-37.
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 Π01 antichain. This result is optimal and has connections to the program of reverse mathematics.
Notre Dame J. Formal Logic, Volume 49, Number 1 (2008), 1-37.
First available in Project Euclid: 6 January 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
Secondary: 03E30: Axiomatics of classical set theory and its fragments 03C62: Models of arithmetic and set theory [See also 03Hxx]
Binns, Stephen; Kjos-Hanssen, Bjørn; Lerman, Manuel; Schmerl, James H.; Solomon, Reed. Self-Embeddings of Computable Trees. Notre Dame J. Formal Logic 49 (2008), no. 1, 1--37. doi:10.1215/00294527-2007-003. https://projecteuclid.org/euclid.ndjfl/1199649898