Journal of Symbolic Logic

A $\Delta^0_2$ Set with No Infinite Low Subset in Either It or Its Complement

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

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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 $\omega$-model of RCA$_0$+ SRT$^2_2$ must contain a nonlow set.

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J. Symbolic Logic, Volume 66, Issue 3 (2001), 1371-1381.

First available in Project Euclid: 6 July 2007

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Downey, Rod; Hirschfeldt, Denis R.; Lempp, Steffen; Solomon, Reed. A $\Delta^0_2$ Set with No Infinite Low Subset in Either It or Its Complement. J. Symbolic Logic 66 (2001), no. 3, 1371--1381.

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