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The Complexity of Classification Problems for Models of Arithmetic

Published online by Cambridge University Press:  15 January 2014

Samuel Coskey
Affiliation:
Mathematics Program, The Cuny Graduate Center, 365 Fifth Avenue, New York, NY 10016-4309, USA, E-mail: scoskey@nylogic.org, E-mail: rkossak@nylogic.org
Roman Kossak
Affiliation:
Mathematics Program, The Cuny Graduate Center, 365 Fifth Avenue, New York, NY 10016-4309, USA, E-mail: scoskey@nylogic.org, E-mail: rkossak@nylogic.org

Abstract

We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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