Geodesic
Relatively recursive expansions II
C. J. Ash1 ; J. F. Knight2 ; T. A. Slaman3
1Department of Mathematics Monash University Clayton, Victoria 3168 Australia
2Mathematics Department University of Notre Dame P.O. BOX 398 Notre Dame, Indiana 46556 U.S.A.
3Department of Mathematics University of Chicago Chicago, Illinois 60637 U.S.A.
Fundamenta Mathematicae, Tome 142 (1993) no. 2, pp. 147-161
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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.
DOI : 10.4064/fm_1993_142_2_1_147_161

C. J. Ash  1   ; J. F. Knight  2   ; T. A. Slaman  3

1 Department of Mathematics Monash University Clayton, Victoria 3168 Australia
2 Mathematics Department University of Notre Dame P.O. BOX 398 Notre Dame, Indiana 46556 U.S.A.
3 Department of Mathematics University of Chicago Chicago, Illinois 60637 U.S.A. 
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C. J. Ash; J. F. Knight; T. A. Slaman. Relatively recursive expansions II. Fundamenta Mathematicae, Tome 142 (1993) no. 2, pp. 147-161. doi: 10.4064/fm_1993_142_2_1_147_161

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