Invariant universality for quandles and fields
Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 1-16
MSC: Primary 03E15; Secondary 12F05, 12F20, 20N99.
DOI: 10.4064/fm862-2-2020
Published online: 8 April 2020
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.
