# Relatively recursive expansions II

Fundamenta Mathematicae (1993)

• Volume: 142, Issue: 2, page 147-161
• ISSN: 0016-2736

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## Abstract

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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.

## How to cite

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Ash, C., Knight, J., and Slaman, Theodore. "Relatively recursive expansions II." Fundamenta Mathematicae 142.2 (1993): 147-161. <http://eudml.org/doc/211978>.

@article{Ash1993,
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.},
author = {Ash, C., Knight, J., Slaman, Theodore},
journal = {Fundamenta Mathematicae},
keywords = {additional relation symbol; recursive infinitary sentence; recursive structure},
language = {eng},
number = {2},
pages = {147-161},
title = {Relatively recursive expansions II},
url = {http://eudml.org/doc/211978},
volume = {142},
year = {1993},
}

TY - JOUR
AU - Ash, C.
AU - Knight, J.
AU - Slaman, Theodore
TI - Relatively recursive expansions II
JO - Fundamenta Mathematicae
PY - 1993
VL - 142
IS - 2
SP - 147
EP - 161
AB - 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.
LA - eng
KW - additional relation symbol; recursive infinitary sentence; recursive structure
UR - http://eudml.org/doc/211978
ER -

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