论文标题
极度最小的坦纳系统III：路径图和稀疏配置
Strongly minimal Steiner Systems III: Path graphs and sparse configurations
论文作者
论文摘要
我们引入了一种统一的证明方法，以获得以下结果。对于以下条件的{\ em每个}，有$ 2^{\ aleph_0} $ steiner系统的家族，满足该条件：i）定理〜2.2.4 ：（扩展\ cite \ cite {chicoetal}）每个steiner triple triple System均为$ \ infty $ sparse，并且具有完美的路径图形，但没有完美的路径； ii）（定理〜5.4.2 ：（扩展\ cite {cameronwebb}）每个steiner $ k $ - 系统（对于$ k = p^n $）是$ 2 $ - 传输，并具有统一的路径图（仅限的循环）; iii）; iii）theorem〜2.1.5：（extected \ 2.1.5 ：（扩展\ cite） （反点数）; iv）定理〜3.6具有明确的准集团结构。在每种情况下，家庭的所有成员都满足相同的完全最小的理论，并且它具有$ \ aleph_0 $可计数的模型和每个不可数的红衣主教的一种模型。
We introduce a uniform method of proof for the following results. For {\em each} of the following conditions, there are $2^{\aleph_0}$ families of Steiner systems, satisfying that condition: i) Theorem~2.2.4: (extending \cite{Chicoetal}) each Steiner triple system is $\infty$-sparse and has a uniform but not perfect path graph; ii) (Theorem~5.4.2: (extending \cite{CameronWebb}) each Steiner $k$-system (for $k=p^n$) is $2$-transitive and has a uniform path graph (infinite cycles only); iii) Theorem~2.1.5: (extending \cite{Fujiwaramitre}, each is anti-Pasch (anti-mitre); iv) Theorem~3.6 has an explicit quasi-group structure. In each case all members of the family satisfy the same complete strongly minimal theory and it has $\aleph_0$ countable models and one model of each uncountable cardinal.
