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September 2008 Classifying model-theoretic properties
Chris J. Conidis
J. Symbolic Logic 73(3): 885-905 (September 2008). DOI: 10.2178/jsl/1230396753

Abstract

In 2004 Csima, Hirschfeldt, Knight, and Soare [1] showed that a set A ≤T 0’ is nonlow2 if and only if A is prime bounding, i.e., for every complete atomic decidable theory T, there is a prime model ℳ computable in A. The authors presented nine seemingly unrelated predicates of a set A, and showed that they are equivalent for Δ02 sets. Some of these predicates, such as prime bounding, and others involving equivalence structures and abelian p-groups come from model theory, while others involving meeting dense sets in trees and escaping a given function come from pure computability theory. As predicates of A, the original nine properties are equivalent for Δ02 sets; however, they are not equivalent in general. This article examines the (degree-theoretic) relationship between the nine properties. We show that the nine properties fall into three classes, each of which consists of several equivalent properties. We also investigate the relationship between the three classes, by determining whether or not any of the predicates in one class implies a predicate in another class.

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Chris J. Conidis. "Classifying model-theoretic properties." J. Symbolic Logic 73 (3) 885 - 905, September 2008. https://doi.org/10.2178/jsl/1230396753

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1160.03012
MathSciNet: MR2444274
Digital Object Identifier: 10.2178/jsl/1230396753

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 3 • September 2008
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