Original Paper

Computable choice functions for computable linear orderings

  1. Manuel Lerman,
  2. Richard Watnick

Article first published online: 3 JUL 2003

DOI: 10.1002/malq.200310053

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Volume 49, Issue 5, pages 485–510, September 2003

Additional Information

How to Cite

Lerman, M. and Watnick, R. (2003), Computable choice functions for computable linear orderings. Mathematical Logic Quarterly, 49: 485–510. doi: 10.1002/malq.200310053

Author Information

  1. Department of Mathematics, University of Connecticut at Stamford, Stamford, CT 06901, U. S. A.

Publication History

  1. Issue published online: 3 JUL 2003
  2. Article first published online: 3 JUL 2003
  3. Manuscript Accepted: 28 MAR 2003
  4. Manuscript Revised: 26 MAR 2003
  5. Manuscript Received: 23 DEC 2002

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Keywords:

  • Computable order-type;
  • linear ordering;
  • choice function

Abstract

A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of order-types, each of which either has finitely many blocks, or has order-type n · η for some integer n.

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