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

by Rod Downey, Denis R. Hirschfeldt, Steffen Lempp, and Reed Solomon

Status: published in the Journal of Symbolic Logic, vol. 66 (2001), pp. 1371 - 1381.

Availability: journal version and preprint

Abstract. We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman, and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem.