Journal of Symbolic Logic

Up to equimorphism, hyperarithmetic is recursive

Antonio Montalbán

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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 ω₁CK 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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J. Symbolic Logic Volume 70, Issue 2 (2005), 360-378.

First available in Project Euclid: 1 July 2005

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Montalbán, Antonio. Up to equimorphism, hyperarithmetic is recursive. J. Symbolic Logic 70 (2005), no. 2, 360--378. doi:10.2178/jsl/1120224717.

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