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Gentzen´s cut-elimination theorem is one of the most important theorems of logic. Removing cuts from formal proofs corresponds to the elimination of intermediary lemmas from mathematical proofs. It is well known that cut-elimination is of nonelementary complexity in general. Aim of this book is to identify classes, where cut-elimination is elementary, i.e fast. The first part describes basic notions of logic, such as sequent calculus, resolution calculus and two methods of cut-elimination, such as Gentzen´s method and the CERES method. It is proved that CERES method nonelementary speeds up Gentzen´s method and in the second part CERES will be used as a tool to identify fast classes and prove elementary cut-elimination on them. This book is self-contained and written in easy way, so no preliminary knowledge is required and all people interested in logic and proof theory can read it.

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Born in Tbilisi, Georgia. He graduated as a Bachelor of Mathematics from the Tbilisi State University in 2007. Then he continued study in Computer Science and got an MSc. degree from the Vienna University of Technology in 2009. Mikheil currently works as a Project Assistant at Institute of Computer Languages, Vienna University of Technology.

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