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Strongly Minimal Steiner Systems II: Coordinatization and Quasigroups

2021/06/25 by Baldwin, John T. · 1 citation
#03C05 (Primary) 03C45 #03C98 (Secondary) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2106.13704

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.

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