Submission date: 25 June 2021

Abstract:

We note that a strongly minimal Steiner k-Steiner system (M,R) from (Baldwin-Paolini 2020) can be `coordinatized' in the sense of (Gantner-Werner 1975) by a quasigroup if k is a prime-power. But for the basic construction this coordinatization is never definable in (M,R). Nevertheless, by refining the construction, if k is a prime power there is a (2,k)-variety of quasigroups which is strongly minimal and definably coordinatizes a Steiner k-system.

Mathematics Subject Classification: 03C05 (Primary) 03C45, 03C98 (Secondary)

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Full text arXiv 2106.13704: pdf, ps.