solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看2649次
A Universal Homogeneous Simple Rank $3$ Matroid. (arXiv:1707.05069v5 [math.LO] UPDATED)
来源于:arXiv
We construct a countably infinite simple rank $3$ matroid $M_*$ which
$\wedge$-embeds every finite simple rank $3$ matroid, and such that every
isomorphism between finite $\wedge$-subgeometries of $M_*$ extends to an
automorphism of $M_*$. We prove that $M_*$ is not $\aleph_0$-categorical, it
has the independence property, it admits a stationary independence relation,
and that $Aut(M_*)$ embeds the symmetric group $Sym(\omega)$. Finally, we use
the free projective extension of $M_*$ to conclude the existence of a countably
infinite projective plane embedding all the finite simple rank $3$ matroids and
whose automorphism group contains $Sym(\omega)$. 查看全文>>