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A Δ20 set with no infinite low subset in either it or its complement

  • Rod Downey (a1), Denis R. Hirschfeldt (a2), Steffen Lempp (a3) and Reed Solomon (a4)

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 must contain a nonlow set.

Corresponding author
Current address: (for Hirschfeldt) Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA, E-mail:
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[1]Cholak, P. A., Jockusch, C. G. Jr., and Slaman, T. A., On the strength of Ramsey's theorem for pairs, to appear in this journal.
[2]Simpson, S. G., Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer–Verlag, Berlin, 1999.
[3]Soare, R. I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer–Verlag, Heidelberg, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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