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Journal of Logic and Computation Advance Access originally published online on August 5, 2008
Journal of Logic and Computation 2009 19(1):145-150; doi:10.1093/logcom/exn031
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

This article appears in the following Journal of Logic and Computation issue: Special Issue: Logic and Computation in the Real World: CiE 2007 [View the issue table of contents]

Original Articles

The Settling Time Reducibility Ordering and {Delta}Formula Sets

Barbara F. Csima

Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
E-mail: csima{at}math.uwaterloo.ca

The settling time reducibility ordering gives an ordering on computably enumerable sets based on their enumerations. The <st ordering is in fact an ordering on c.e. sets, since it is independent of the particular enumeration chosen. In this article, we show that it is not possible to extend this ordering in an approximation-independent way to {Delta}Formula sets in general, or even to n-c.e. sets for any fixed n ≥ 3.

Keywords: Computability theory; {Delta}Formula sets; computable approximations



References

  1. Cooper SB. Computability Theory. (2004) Boca Raton, FL: Chapman & Hall/CRC.
  2. Csima BF. Comparing c.e. sets based on their settling times. Cooper SB, Löwe B, Sorbi A, eds. (2007) Springer. 196–204. CiE. Vol. 4497 of Lecture Notes in Computer Science.
  3. Csima BF, Soare RI. Computability results used in differential geometry. Journal of Symbolic Logic (2006) 71:1394–1410.[CrossRef][Web of Science]
  4. Soare RI. Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. (1987) Berlin: Springer-Verlag. (Perspectives in Mathematical Logic).
  5. Soare RI. Computability theory and differential geometry, Bulletin of Symbolic Logic (2004) 10:457–486.[CrossRef][Web of Science]
  6. Soare RI. Computability Theory and Applications. (in preparation).

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This Article
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Right arrow Full Text (PDF)
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