Journal of Symbolic Logic

Up to equimorphism, hyperarithmetic is recursive

Antonio Montalbán

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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 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.

Article information

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

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1120224717

Digital Object Identifier
doi:10.2178/jsl/1120224717

Mathematical Reviews number (MathSciNet)
MR2140035

Zentralblatt MATH identifier
1089.03036

Citation

Montalbán, Antonio. Up to equimorphism, hyperarithmetic is recursive. Journal of Symbolic Logic 70 (2005), no. 2, 360--378. doi:10.2178/jsl/1120224717. http://projecteuclid.org/euclid.jsl/1120224717.


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