Classes of structures with no intermediate isomorphism problems

Antonio Montalbán

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arXiv · 1309.3815

Classes of structures with no intermediate isomorphism problems

Antonio Montalbán

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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 on 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 on a cone.

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BibTeX RIS

Antonio Montalbán. 2013-09-16. Classes of structures with no intermediate isomorphism problems. https://arxiv.org/abs/1309.3815

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