Relatively recursive expansions II

Volume 142 / 1993

C. J. Ash, J. F. Knight, T. A. Slaman Fundamenta Mathematicae 142 (1993), 147-161 DOI: 10.4064/fm_1993_142_2_1_147_161

Abstract

In [AK], we asked when a recursive structure A and a sentence φ, with a new relation symbol, have the following property: for each ℬ≅ A there is a relation S such that S is recursive relative to ℬ and ℬ,S)⊨ φ. Here we consider several related properties, in which there is a uniform procedure for determining S from ℬ ≅A, or from ℬ,¯b)≅(A,ā), for some fixed sequence of parameters ā from A; or in which ℬ and S are required to be recursive. We investigate relationships between these properties, showing that for certain kinds of sentences φ, some of these properties do or do not imply others. Many questions are left open.

Authors

  • C. J. AshDepartment of Mathematics
    Monash University
    Clayton, Victoria 3168
    Australia
  • J. F. KnightMathematics Department
    University of Notre Dame
    P.O. BOX 398
    Notre Dame, Indiana 46556
    U.S.A.
  • T. A. SlamanDepartment of Mathematics
    University of Chicago
    Chicago, Illinois 60637
    U.S.A.

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