δ-Uniformly decidable sets and turing machines

  • Adriana Popovici
  • Dan Popovici
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)


We give a characterization of the archimedean fields in which nontrivial δ-uniform decidable sets exist. More exactly, after we introduce a notion of Turing closure of an archimedean field we prove that such a field posseses nontrivial δ-uniformly decidable sets if and only if it is not Turing closed. Moreover, if a function is δ-uniformly computable on a Turing closed field then it is rational over each of the connected components induced on the halting set by the reals. Finally, given a field which is not Turing closed, we obtain as a consequence that there exists a δ-uniform machine computing a total function which is not rational.


Turing Machine Minimum Polynomial Total Function Dense Subspace Input Tape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Adriana Popovici
    • 1
  • Dan Popovici
    • 2
  1. 1.Department of Computer ScienceWest University of TimişoaraTimişoaraRomania
  2. 2.Department of MathematicsWest University of TimişoaraTimişoaraRomania

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