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# Up to Equimorphism, Hyperarithmetic Is Recursive

Antonio Montalbán
The Journal of Symbolic Logic
Vol. 70, No. 2 (Jun., 2005), pp. 360-378
Stable URL: http://www.jstor.org/stable/27588367
Page Count: 19
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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 $\omega _{1}^{\mathit{CK}}$ 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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