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CLASSES OF STRUCTURES WITH NO INTERMEDIATE ISOMORPHISM PROBLEMS

Published online by Cambridge University Press:  22 January 2016

ANTONIO MONTALBÁN
ANTONIO MONTALBÁN*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA BERKELEY, USAE-mail: antonio@math.berkeley.eduURL: www.math.berkeley.edu/∼antonio
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Abstract

We say that a theory T is intermediate under effective reducibility if the isomorphism problems among its computable models is neither hyperarithmetic nor on top under effective reducibility. We prove that if an infinitary sentence T is uniformly effectively dense, a property we define in the paper, then no extension of it is intermediate, at least when relativized to every oracle in a cone. As an application we show that no infinitary sentence whose models are all linear orderings is intermediate under effective reducibility relative to every oracle in a cone.

Keywords

Vaught’s conjectureeffective reducibilityequivalence relations

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 127 - 150
Copyright
Copyright © The Association for Symbolic Logic 2016 

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