Strongly Minimal Steiner Systems II: Coordinatization and Quasigroups
Logic
2023-02-22 v2
Abstract
We note that a strongly minimal Steiner -Steiner system from (Baldwin-Paolini 2020) can be `coordinatized' in the sense of (Gantner-Werner 1975) by a quasigroup if is a prime-power. But for the basic construction this coordinatization is never definable in . Nevertheless, by refining the construction, if is a prime power there is a -variety of quasigroups which is strongly minimal and definably coordinatizes a Steiner -system.
Cite
@article{arxiv.2106.13704,
title = {Strongly Minimal Steiner Systems II: Coordinatization and Quasigroups},
author = {John T. Baldwin},
journal= {arXiv preprint arXiv:2106.13704},
year = {2023}
}
Comments
14 pages Version II: different format with much narrower pages 23 pages submitted on Feb. 21, 2023 a file created Dec. 23, 2022. Corrected typos and some technical arguments. No change in major results