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1 results

  • MAXIMAL COMPUTABILITY STRUCTURES

  • ZVONKO ILJAZOVIĆ, LUCIJA VALIDŽIĆ
  • Journal:
    Bulletin of Symbolic Logic / Volume 22 / Issue 4 / December 2016
    Published online by Cambridge University Press:
    30 December 2016, pp. 445-468
    Print publication:
    December 2016

  • A computability structure on a metric space is a set of sequences which satisfy certain conditions. Of a particular interest are those computability structures which contain a dense sequence, so called separable computability structures. In this paper we observe maximal computability structures which are more general than separable computability structures and we examine their properties. In particular, we examine maximal computability structures on subspaces of Euclidean space, we give their characterization and we investigate conditions under which a maximal computability structure on such a space is unique. We also give a characterization of separable computability structures on a segment.