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Up to equimorphism, hyperarithmetic is recursive

Published online by Cambridge University Press:  12 March 2014

Antonio Montalbán
Antonio Montalbán*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, E-mail: antonio@math.cornell.edu URL: www.math.cornell.edu/~antonio
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Abstract

Two linear orderings are equimorphic if each can be embedded into the other. We prove that every hyperarithmetic linear ordering is equimorphic to a recursive one.

On the way to our main result we prove that a linear ordering has Hausdorff rank less than if and only if it is equimorphic to a recursive one. As a corollary of our proof we prove that, given a recursive ordinal α, the partial ordering of equimorphism types of linear orderings of Hausdorff rank at most α ordered by embeddablity is recursively presentable.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005, pp. 360 - 378
Copyright
Copyright © Association for Symbolic Logic 2005

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