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.

中文翻译：

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场的方程理论

如果每个可定义的集合都是方程实例的布尔组合，则一阶理论是方程的，即，实例的有限交集的族具有降链条件的公式的布尔组合。平等是对稳定性的加强。我们展示了代数闭域的适当扩展理论和任意不完美度的可分离闭域理论的等式性。