Model Theory of analytic structures and quasi-minimal fields

有两个结果：第一个是关于“周氏定理”的。代数几何中的这一著名定理声称，射影空间中的任何解析簇实际上都是代数定义的。牛津大学的Peatfield博士和Zilber教授在解析Zariski结构情形下证明了一个Chow类型的定理。我们证明了他们的定理的一个推广。第二个是将Richardson定理应用于具有伪幂的代数闭域，称为Kex。理查森定理给出了零集到代数指数方程组的不可约分解。代数指数方程是允许有限个指数函数出现在其中的代数方程。我们证明了同样的说法在Kex也是成立的。

There are two results : the first one is concerning "Chow's Theorem". This famous theorem in algebraic geometry claims that any analytic variety in projective space is in fact algebraically defined. Dr. Peatfield and Prof. Zilber at Oxford University had proved a Chow type theorem in an analytic Zariski structure situation. We proved a generalization of their theorem.The second one is to apply Richardson's Theorem to algebraically closed fields equipped with a pseudo-exponentiation called Kex. Richardson's theorem gives irreducible decompositions of the zero sets to a system of algebraic-exponential equations. An algebraic-exponential equation is an algebraic equation allowing finitely may exponential functions to appear in it. We proved that the same statement holds in Kex.