Abstract
In these notes we sketch a proof of the model completeness of the real exponential field. We begin with an introduction to the various Preparation Theorems required for the proof as well as a discussion of polynomially bounded, o-minimal structures. We then discuss the appropriate valuation theoretic setting and show how the so-called Valuation Inequality leads to the desired result. We conclude with some speculative remarks on the model theory of the complex exponential field.
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Wilkie, A.J. (2014). Lectures on the Model Theory of Real and Complex Exponentiation. In: Model Theory in Algebra, Analysis and Arithmetic. Lecture Notes in Mathematics(), vol 2111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54936-6_3
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DOI: https://doi.org/10.1007/978-3-642-54936-6_3
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