K-Trivial Closed Sets and Continuous Functions View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2007

AUTHORS

George Barmpalias , Douglas Cenzer , Jeffrey B. Remmel , Rebecca Weber

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 class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.

PAGES

135-145

References to SciGraph publications

  • 2006. Random Closed Sets in LOGICAL APPROACHES TO COMPUTATIONAL BARRIERS
  • 2008-05. Algorithmic randomness of continuous functions in ARCHIVE FOR MATHEMATICAL LOGIC
  • 2003-08. Density of the Medvedev lattice of Π01 classes in ARCHIVE FOR MATHEMATICAL LOGIC
  • 2010. Algorithmic Randomness and Complexity in NONE
  • Book

    TITLE

    Computation and Logic in the Real World

    ISBN

    978-3-540-73000-2
    978-3-540-73001-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-540-73001-9_14

    DOI

    http://dx.doi.org/10.1007/978-3-540-73001-9_14

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1049137265


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