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

Published online by Cambridge University Press:  12 March 2014

Rod Downey ,
Denis R. Hirschfeldt ,
Steffen Lempp  and
Reed Solomon
Rod Downey
Affiliation:
School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail: [email protected]
Denis R. Hirschfeldt*
Affiliation:
School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail: [email protected]
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail: [email protected]
Reed Solomon
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail: [email protected]
*
Current address: (for Hirschfeldt) Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA, E-mail: [email protected]
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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 must contain a nonlow set.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1371 - 1381
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[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.Google Scholar
[2]Simpson, S. G., Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer–Verlag, Berlin, 1999.CrossRefGoogle Scholar
[3]Soare, R. I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer–Verlag, Heidelberg, 1987.CrossRefGoogle Scholar