\chapter*{Acknowledgements}
I would like to thank my supervisor Thierry Coquand for giving me a
chance to work on this interesting topic. I would also like to thank
Andrea Vezzosi for some very long and very insightful meetings during
the project. It is fascinating and almost uncanny how quickly Andrea
can conjure up various proofs.  I also want to recognize the support
of Knud Højgaards Fond who graciously sponsored me with a 20.000 DKK
scholarship which helped toward sponsoring the two years I have spent
studying abroad. I would also like to give a warm thanks to my fellow
students Pierre~Kraft and Nachiappan~Valliappan who have made the time
spent working on the thesis way more enjoyable. Lastly I would like to
give a special thanks to Valentina~Méndez who have been a great moral
support throughout the whole process.
