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A Δ02 Set with No Infinite Low Subset in Either It or Its Complement

Rod Downey, Denis R. Hirschfeldt, Steffen Lempp and Reed Solomon
The Journal of Symbolic Logic
Vol. 66, No. 3 (Sep., 2001), pp. 1371-1381
DOI: 10.2307/2695113
Stable URL: http://www.jstor.org/stable/2695113
Page Count: 11
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A Δ02 Set with No Infinite Low Subset in Either It or Its Complement
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Abstract

We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every ω-model of RCA0+ SRT22 must contain a nonlow set.

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