Unimodular Minimal Structures
Unimodular Minimal Structures
复制标题
幺模最小结构
DOI：
10.1112/jlms/s2-46.3.385
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发表时间：
1992
影响因子：
1.2
通讯作者：
E. Hrushovski
中科院分区：
文献类型：
--
作者：
E. Hrushovski
一个强极小结构D称为幺模的，如果任意两个具有相同定义域和值域的有限对一映射具有相同的度;也就是说，如果f 4：（f->>· V处处是f c 4-to-1，则kx = kc，.定理幺模强极小结构是局部模的。这扩展了Zil'ber关于局部有限强极小集的定理，Urbanik关于具有Steinitz性质的自由代数的定理，并且也适用于N 0-范畴稳定理论中的极小类型。
A strongly minimal structure D is called unimodular if any two finite-to-one maps with the same domain and range have the same degree; that is if/4: (/-»• V is everywhere fc4-to-l, then kx = kc,. THEOREM. Unimodular strongly minimal structures are locally modular. This extends Zil'ber's theorem on locally finite strongly minimal sets, Urbanik's theorem on free algebras with the Steinitz property, and applies also to minimal types in N0-categorical stable theories.