Brooke-Taylor, AD orcid.org/0000-0003-3734-0933, Calderoni, F and Miller, SK (2020) Invariant universality for quandles and fields. Fundamenta Mathematicae. ISSN 0016-2736
Abstract
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are invariantly universal. This notion from the theory of Borel reducibility states that any analytic quasi-order on a standard Borel space essentially appears as the restriction of the embeddability relation to an isomorphism-invariant Borel set. As an intermediate step we show that the embeddability relation of countable quandles is a complete analytic quasi-order.
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Copyright, Publisher and Additional Information: | © Instytut Matematyczny PAN, 2020. This is an author produced version of an article published in Fundamenta Mathematicae. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | analytic quasi-orders, invariant universality, quandles, fields | ||||
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 18 Feb 2020 14:45 | ||||
Last Modified: | 17 Apr 2020 02:36 | ||||
Status: | Published online | ||||
Publisher: | Polish Academy of Sciences, Institute of Mathematics | ||||
Identification Number: | https://doi.org/10.4064/fm862-2-2020 |