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Journal of Logic and Computation Advance Access originally published online on July 18, 2008
Journal of Logic and Computation 2009 19(1):77-87; doi:10.1093/logcom/exn028
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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

Pseudojumps and Formula Classes*

Douglas Cenzer

Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611, USA
E-mail: cenzer{at}math.ufl.edu

Geoffrey Laforte

Department of Mathematics and Statistics, University of West Florida, Pensacola, Florida 32514, USA
E-mail: glaforte{at}uwf.edu

Guohua Wu

School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798
E-mail: guohua{at}ntu.edu.sg

Received 26 September 2007.


  Abstract

For a pseudojump VX and a Formula class P, we consider properties of the set {VX:X isin P}.We show that if P is Medvedev complete or if P has positive measure, and Ø' ≤T C, then there exists X isin P with VX {equiv}T C. We examine the consequences when VX is Turing incomparable with VY for X != Y in P and when Formula for all X, Y isin P. Finally, we give a characterization of the jump in terms of Formula classes.

Keywords: Computability; {Pi}Formula Classes

*Support for this research was provided by National Science Foundation awards DMS 0532644 and DMS 0652732.


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