Cell Decompositions of C-Minimal Structures
Cell Decompositions of C-Minimal Structures
复制标题
C-最小结构的细胞分解
DOI：
10.1016/0168-0072(94)90064-7
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
D. Macpherson
中科院分区：
文献类型：
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作者：
Deirdre Haskell;D. Macpherson
C-极小性是 o-极小性的变体，其中结构携带可在树的最大链集合上以自然方式解释的三元关系，而不是线性排序。讨论了这个概念，证明了 C 最小结构的单元分解定理，并引入了维数概念。结果表明，C 极小域是精确赋值的代数闭域。还表明，如果某些特定的“坏”函数不可定义，则代数闭包具有交换性质，并且对于可定义的集合，维数与代数闭包获得的等级一致。
C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure.