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In this thesis, we present the construction of fields with functions which are faster than every iterated exponential function. This introduction will describe what we mean by “construction”, “faster than” and “exponential function”. By doing this, we hope to give the reader a good idea of what he can expect from this thesis, and we hope to provide a motivation for the presented work. Moreover, this introduction will serve as a guide to help the reader through the different parts of the thesis.
We start by explaining some basic concepts and by presenting the main results. We go on to summarize what is known about super-exponential functions. The third part of this introduction will motivate the given construction. Then we will come to the “road map” of the thesis: we give a short summary of each of the forthcoming chapters, thus equipping a possible reader with an orientation guide. This will be of particular interest since some chapters are rather technical, and there is a real danger of losing the overview when working through the unavoidable details. Finally, we list some of the notations used.