再论Frobenius映射推导的模型论
Model theory of derivations of the Frobenius map revisited
摘要：
我们证明了一些结果的模型论的领域与推导的Frobenius映射，特别是该理论的模型伴侣是公理化的公理伍德所使用的理论$\operatorname{DCF}_p$的情况下，它消除了量词后，增加了逆的Frobenius映射的语言。这进一步证明了[4]的结论。作为副产品，我们得到了一个新的几何公理化的模型伴侣。一路上，我们还证明了一个量词消除的结果，这在一个更一般的情况下，我们建议一种方式给予“一维”公理化模型同伴的一些理论领域的运营商。
英文摘要：
We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory $\operatorname{DCF}_p$ and that it eliminates quantifiers after adding the inverse of the Frobenius map to the language. This strengthens the results from [4]. As a by-product, we get a new geometric axiomatization of this model companion. Along the way we also prove a quantifier elimination result, which holds in a much more general context and we suggest a way of giving "one-dimensional" axiomatizations for model companions of some theories of fields with operators.
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