Up to Equimorphism, Hyperarithmetic Is Recursive

Journal of Symbolic Logic 70 (2):360 - 378 (2005)
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 $\omega _{1}^{\mathit{CK}}$ 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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DOI 10.2178/jsl/1120224717
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References found in this work BETA
The Metamathematics of Scattered Linear Orderings.P. Clote - 1989 - Archive for Mathematical Logic 29 (1):9-20.

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On the Equimorphism Types of Linear Orderings.Antonio Montalbán - 2007 - Bulletin of Symbolic Logic 13 (1):71-99.

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