Ordered exponential field

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.
Definition.
An exponential formula_1 on an ordered field formula_2 is a strictly increasing isomorphism of the additive group of formula_2 onto the multiplicative group of positive elements of formula_2. The ordered field formula_5 together with the additional function formula_6 is called an ordered exponential field.
Formally exponential fields.
A formally exponential field, also called an exponentially closed field, is an ordered field that can be equipped with an exponential formula_1. For any formally exponential field formula_2, one can choose an exponential formula_1 on formula_2 such that 
formula_16 for some natural number formula_17.