An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency Proofs

About Paolo MancosuRichard ZachSergio Galvan

Paolo Mancosu is Willis S. and Marion Slusser Professor of Philosophy at the University of California at Berkeley. He is the author of numerous articles and books in logic and philosophy of mathematics. During his career he has taught at Stanford Oxford and Yale. He was awarded a fellowship at the Wissenschaftskolleg zu Berlin in 1997-1998 a stipendiary position as Directeur de recherche invité; au CNRS in Paris in 2004-2005 a Guggenheim Fellowship in 2008-2009 a position as member at the Institute of Advanced Study in Princeton in 2009 a visiting professorship as LMU-UCB Research in the Humanities at LMU in 2014 and a Humboldt Research Award in 2017-2018. Sergio Galvan is emeritus Professor of Logic at the Catholic University of Milan Italy. His main areas of research are proof-theory and philosophical logic. In the first area he focuses on sequent calculi and natural deduction the metamathematics of arithmetic systems (from Q to PA) Gödel's incompleteness theorems and Gentzen's cut-elimination theorem. In the second area his major interest is in the philosophical interpretations (deontic epistemic and metaphysical) of modal logic. Recently he has been working on the relationships between formal proof and intuition in mathematics and on the metaphysics of essence and the ontology of possibilia. Richard Zach is Professor of Philosophy at the University of Calgary Canada. He works in logic history of analytic philosophy and the philosophy of mathematics. In logic his main interests are non-classical logics and proof theory. He has also written on the development of formal logic and historical figures associated with this development such as Hilbert Gödel and Carnap. He has held visiting appointments at the University of California Irvine McGill University and the University of Technology Vienna.