Relatively recursive expansions II

• Autorzy: C. J. Ash , J. F. Knight , Theodore A. Slaman
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 142
• Numer: 2
• Strony: 147-161

Daty

wydano

1993

otrzymano

1992-02-11

poprawiono

1992-11-16

Twórcy

autor

C. J. Ash

• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia

autor

J. F. Knight

• Mathematics Department, University of Notre Dame, P.O. Box 398, Notre Dame, Indiana 46556, U.S.A.

autor

Theodore A. Slaman

• Department of Mathematics, University of Chicago, Chicago, Illinois 60637, U.S.A.

Bibliografia

• [AK] C. J. Ash and J. F. Knight, Relatively recursive expansions I, Fund. Math. 140 (1992), 137-155.
• [AKMS] C. J. Ash, J. F. Knight, M. Manasse, and T. A. Slaman, Generic copies of countable structures, Ann. Pure Appl. Logic 42 (1989), 195-205.