Turing Degrees of Isomorphism Types of Algebraic Objects

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dc.creatorCalvert, Wesley
dc.creatorHarizanov, Valentina
dc.creatorShlapentokh, Alexandra
dc.date2005-07-06
dc.date.accessioned2026-07-07T05:21:27Z
dc.date.available2026-07-07T05:21:27Z
dc.descriptionThe Turing degree spectrum of a countable structure $\mathcal{A}$ is the set of all Turing degrees of isomorphic copies of $\mathcal{A}$. The Turing degree of the isomorphism type of $\mathcal{A}$, if it exists, is the least Turing degree in its degree spectrum. We show there are countable fields, rings, and torsion-free abelian groups of arbitrary rank, whose isomorphism types have arbitrary Turing degrees. We also show that there are structures in each of these classes whose isomorphism types do not have Turing degrees.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0507128
dc.identifierhttp://arxiv.org/abs/math/0507128
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75699
dc.subjectLogic
dc.subjectCommutative Algebra
dc.subjectNumber Theory
dc.titleTuring Degrees of Isomorphism Types of Algebraic Objects
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