English

Invariant universality for quandles and fields

Logic 2020-07-21 v2

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.

Keywords

Cite

@article{arxiv.1706.08142,
  title  = {Invariant universality for quandles and fields},
  author = {Andrew D. Brooke-Taylor and Filippo Calderoni and Sheila K. Miller},
  journal= {arXiv preprint arXiv:1706.08142},
  year   = {2020}
}
R2 v1 2026-06-22T20:29:01.104Z