EQUATIONAL THEORIES OF FIELDS
EQUATIONAL THEORIES OF FIELDS
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场方程理论
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Ziegler
中科院分区：
文献类型：
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作者：
A. Martin;M. Ziegler
如果每一个可定义的集合都是方程实例的布尔组合，即公式的布尔组合，使得实例的有限交集具有降链条件，则一阶理论是等式。平等性是稳定性的加强。证明了代数闭域的真扩张理论和任意不完备度的可分闭域理论的等价性。
Abstract A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.