Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-30T15:53:37.791Z Has data issue: false hasContentIssue false
  • English
  • Français

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: downey@mcs.vuw.ac.nz
Denis R. Hirschfeldt*
Affiliation:
School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand, E-mail: drh@mcs.vuw.ac.nz
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail: lempp@math.wisc.edu
Reed Solomon
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA, E-mail: rsolomon@math.wisc.edu
*
Current address: (for Hirschfeldt) Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA, E-mail: drh@math.uchicago.edu
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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