Foremost, I would like to thank my supervisor, Prof. Andrei Voronkov, who shared with me a lot of his expertise and research insight. He quickly became for me the role model of a successful researcher in the field. I also like to express my gratitude to Dr.-Ing. Renate A. Schmidt, whose thoughtful advise often served to give me a sense of direction during my PhD studies. And I am deeply grateful to the National Council of Science and Technology in México (CONACYT) for the trust and support that they gave me in order to study in the UK.
It is difficult to overstate my appreciation to Prof. Mauricio Osorio, who first brought me into the world of research and with whom I began to learn about mathematical logic and theoretical computer science. Not only a great mentor and colleague, he has also been a cornerstone in my professional development.
I wish to thank everybody with whom I have shared experiences in life. From the people who first persuaded and got me interested into the study of mathematics, specially those who also played a significant role in my life, to those which with the gift of their company made my days more enjoyable and worth living.
I am tempted to individually thank all of my friends which, from my childhood until graduate school, have joined me in the discovery of what is life about and how to make the best of it. However, because the list might be too long and by fear of leaving someone out, I will simply say thank you very much to you all.
Some of you are, anyway, quite lucky: thank you Luis and Enrique (los Novatos), Ariadna, Joachim, Gaby and Héctor for being some of my very best friends.
I cannot finish without saying how grateful I am with my family: grandparents, uncles, aunts, cousins and nephews all have given me a loving environment where to develop. Particular thanks, of course, to Daniel and Rodrigo my brothers and best mates. Lastly, and most importantly, I wish to thank my parents, Maria Eugenia and Juan Antonio. They have always supported and encouraged me to do my best in all matters of life. To them I dedicate this thesis.