The exponential rank of nonarchimedean exponential fields
Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by a paper of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become a basic tool in the theory of ordered fields and real algebraic geometry. In this paper, we take a further step by adding an exponential function to the ordered field.