## Intervals without critical triples |

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3's parent node 7-expansionary stage Action applies at stage appropriate computable w-ordering Assume bo and bi bound a weak child Cholak and Downey Choose some appropriate computably enumerable degrees computably enumerable set computably enumerable Turing construct intervals Cornell University define Downey and Shore enumerable tt degrees enumerable Turing degrees exist let form a critical form a weak Hence higher priority induction infinitely many stages injure Me,x intervals of computably Lachlan last stage Lattice embeddings lattice M5 layers Lemma Lempp length 2k length of agreement Let 2t low2 degree meet TZe negative requirement node is called node of length nonbounding nondecreasing nonlow2 peel back positive requirements Proof putably enumerable degrees recursively enumerable degrees redefine restraint function rx(s Slaman started by stage strategy as described strategy has outcome Suppose Theorem true path Turing machine upper semilattice weak critical triple Weinstein 1988 witness w exists