We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of “tame” differential fields. We state several characterizations and exhibit plenty of examples and applications. Our results strongly indicate that differentially large fields will play a key role in differential field arithmetic. For instance, we characterize differential largeness in terms of being existentially closed in their power series field (furnished with natural derivations), we give explicit constructions of differentially large fields in terms of iterated powers series, we prove that the class of differentially large fields is elementary, and we show that differential largeness is preserved under algebraic extensions, therefore showing that their algebraic closure is differentially closed.

我们引入了具有多个通勤导数的域的微分大小的概念（类似于域的大小）。我们为这一类新的“驯服”微分场奠定了基础。我们陈述了几个特征并展示了大量的示例和应用。我们的结果强烈表明，微分大域将在微分域算法中发挥关键作用。例如，我们用幂级数域中的存在封闭性来描述微分大度（提供自然导数），我们根据迭代幂级数给出微分大域的显式构造，我们证明微分大域的类是初等的，并且我们证明了在代数扩张下保留了微分大小，因此表明它们的代数闭包是微分闭的。