Definable sets in algebraically closed valued fields: elimination of imaginaries
Definable sets in algebraically closed valued fields: elimination of imaginaries
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代数闭值域中的可定义集合：消除虚数
DOI：
10.1515/crelle.2006.066
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
D. Macpherson
中科院分区：
文献类型：
--
作者：
Deirdre Haskell;E. Hrushovski;D. Macpherson
本文证明了：若K是赋值环为R的代数闭值域，则若Kn中的某些可定义R-子模的陪集为元素的类被加，则Th（K）有消元。证明涉及的发展理论的独立性一元类型，发挥作用的1型，其次是分析细菌的可定义的功能，从一元集的排序。
Abstract It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in Kn of certain definable R-submodules of Kn (for all ). The proof involves the development of a theory of independence for unary types, which play the role of 1-types, followed by an analysis of germs of definable functions from unary sets to the sorts.