Isolation and lattice embeddings

Journal of Symbolic Logic 67 (3):1055-1064 (2002)
Say that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o', caps a to o. Thus, {o, c, d, o'} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of N5 embedding
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DOI 10.2178/jsl/1190150148
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