Restricted analytic valued fields with partial exponentiation

Abstract

Non-archimedean models of the theory of the real ordered field with restricted analytic functions may not support a total exponential function, but they always have partial exponentials defined in certain convex subrings. On face of this, we study the first order theory of non-archimedean ordered valued fields with all restricted analytic functions and an exponential function defined in the valuation ring, which extends the restricted analytic exponential. We obtain model completeness and other desirable properties for this theory. In particular, any model embeds in a model where the partial exponential extends to a total one.