K-Trivial Closed Sets and Continuous Functions

  • George Barmpalias
  • Douglas Cenzer
  • Jeffrey B. Remmel
  • Rebecca Weber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

Abstract

We investigate the notion of K-triviality for closed sets and continuous functions. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial \(\Pi^0_1\) class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.

Keywords

Computability Randomness \(\Pi^0_1\) Classes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • George Barmpalias
    • 1
  • Douglas Cenzer
    • 2
  • Jeffrey B. Remmel
    • 3
  • Rebecca Weber
    • 4
  1. 1.School of Mathematics, University of Leeds, Leeds LS2 9JTEngland
  2. 2.Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611 
  3. 3.Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112 
  4. 4.Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551 

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