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Is the theory of partial differential fields a first-order or higher-order logic theory? Is the theory of differential fields already equipped with partial derivatives? I was told that the General Theory of Relativity is at least a second-order logic theory, because it involves solutions of partial derivatives -- is this true? If so, does that mean Maxwell's Equations are also second-order at least as it requires calculating partial derivatives as well?

Thanks!

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    @ZhenLin Please consider converting your comments into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes).2013-10-10

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