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Π10 classes and strong degree spectra of relations

Published online by Cambridge University Press:  12 March 2014

John Chisholm ,
Jennifer Chubb ,
Valentina S. Harizanov ,
Denis R. Hirschfeldt ,
Carl G. Jockusch Jr. ,
Timothy McNicholl  and
Sarah Pingrey
John Chisholm
Affiliation:
Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA, E-mail: JA-Chisholm@wiu.edu
Jennifer Chubb
Affiliation:
Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA, E-mail: jchubb@gwu.edu
Valentina S. Harizanov
Affiliation:
Department of Mathematics, The George Washington University, Washington, DC. 20052, USA, E-mail: harizanv@gwu.edu
Denis R. Hirschfeldt
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA, E-mail: drh@math.uchicago.edu
Carl G. Jockusch Jr.
Affiliation:
Department of Mathematics, University of Illinois, 1409 W Green St.. Urbana, IL 61801, USA, E-mail: jockusch@math.uiuc.edu
Timothy McNicholl
Affiliation:
Department of Mathematics, Lamar University, Beaumont Texas 77710, USA, E-mail: timothy.h.mcnicholl@gmail.com
Sarah Pingrey
Affiliation:
Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA, E-mail: spingrey@gwu.edu
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Abstract

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable subsets of 2ω and Kolmogorov complexity play a major role in the proof.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 1003 - 1018
Copyright
Copyright © Association for Symbolic Logic 2007

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