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.
@article{bwmeta1.element.bwnjournal-article-fmv142i2p147bwm,
author = {C. Ash and J. Knight and Theodore Slaman},
title = {Relatively recursive expansions II},
journal = {Fundamenta Mathematicae},
volume = {142},
year = {1993},
pages = {147-161},
zbl = {0809.03024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p147bwm}
}
Ash, C.; Knight, J.; Slaman, Theodore. Relatively recursive expansions II. Fundamenta Mathematicae, Tome 142 (1993) pp. 147-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p147bwm/
[00000] [AK] C. J. Ash and J. F. Knight, Relatively recursive expansions I, Fund. Math. 140 (1992), 137-155. | Zbl 0809.03023
[00001] [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. | Zbl 0678.03012