Advances in proof theory / edited by Reinhard Kahle, Thomas Strahm, Thomas Studer.

Format:

Book

Contributor:

Kahle, Reinhard., Editor.

Strahm, Thomas., Editor.

Studer, Thomas, Editor.

Series:

Progress in Computer Science and Applied Logic, 2297-0576 ; 28

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Logic.

Mathematical Logic and Foundations.

Local Subjects:

Mathematical Logic and Foundations.

Logic.

Physical Description:

1 online resource (430 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Summary:

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The 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. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. 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. .

Contents:

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.

Notes:

"Advances in proof theory was the title of a symposium organized on the occasion of the 60th birthday of Gerhard J ä ger. The meeting took place on December 13 and 14, 2013, at the University of Bern, Switzerland."

Includes bibliographical references at the end of each chapters.

ISBN:

3-319-29198-X