In mathematics, an ordered exponential field is an ordered field together with a function which generalises the idea of exponential functions on the ordered field of real numbers.
An exponential on an ordered field is a strictly increasing isomorphism of the additive group of onto the multiplicative group of positive elements of . The ordered field together with the additional function is called an ordered exponential field.
A formally exponential field, also called an exponentially closed field, is an ordered field that can be equipped with an exponential . For any formally exponential field , one can choose an exponential on such that for some natural number .[3]