Advances in Proof Theory, Softcover reprint of the original 1st ed. 2016 Progress in Computer Science and Applied Logic Series, Vol. 28

?Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science. 

W. Buchholz: A survey on ordinal notations around the Bachmann-Howard ordinal.- A. Cantini: About truth and types.- R. Dyckhoff: Intuitionistic decision procedures since Gentzen.- S. Feferman: The operational perspective.- R. Gore: Formally verified proof-theory using Isabelle/HOL.- P. Minari: Analytic equational proof systems for combinatory logic and lambda calculus.- W. Pohlers: From subsystems of classical analysis to subsystems of set theory - a personal account.- M. Rathjen: Ordinal analysis and witness extraction.- P.  Schuster: Logic completeness via open induction.- H. Schwichtenberg: On the computational content of Higman's lemma.- P.  Schroeder-Heister: TBA.- A. Setzer: TBA.- S. Wainer: On weak "pointwise" induction, and a miniaturized predicativity.

This book contains state-of-the-art contributions to various topics in Proof Theory The papers range from traditional mathematical proof theory via constructive mathematics to applications in computer science This volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years Includes supplementary material: sn.pub/extras