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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

2016 | OriginalPaper | Buchkapitel

A Survey on Ordinal Notations Around the Bachmann-Howard Ordinal

Wilfried Buchholz

2016 | OriginalPaper | Buchkapitel

About Truth and Types

Andrea Cantini

2016 | OriginalPaper | Buchkapitel

Lindenbaum’s Lemma via Open Induction

Francesco Ciraulo, Davide Rinaldi, Peter Schuster

2016 | OriginalPaper | Buchkapitel

Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory

Jacob Cook, Michael Rathjen

2016 | OriginalPaper | Buchkapitel

Machine-Checked Proof-Theory for Propositional Modal Logics

Jeremy E. Dawson, Rajeev Goré, Jesse Wu

2016 | OriginalPaper | Buchkapitel

Intuitionistic Decision Procedures Since Gentzen

Roy Dyckhoff

2016 | OriginalPaper | Buchkapitel

The Operational Perspective: Three Routes

Solomon Feferman

2016 | OriginalPaper | Buchkapitel

Some Remarks on the Proof-Theory and the Semantics of Infinitary Modal Logic

Pierluigi Minari

2016 | OriginalPaper | Buchkapitel

From Subsystems of Analysis to Subsystems of Set Theory

Wolfram Pohlers

2016 | OriginalPaper | Buchkapitel

Restricting Initial Sequents: The Trade-Offs Between Identity, Contraction and Cut

Peter Schroeder-Heister

2016 | OriginalPaper | Buchkapitel

Higman’s Lemma and Its Computational Content

Helmut Schwichtenberg, Monika Seisenberger, Franziskus Wiesnet

2016 | OriginalPaper | Buchkapitel

How to Reason Coinductively Informally

Anton Setzer

2016 | OriginalPaper | Buchkapitel

Pointwise Transfinite Induction and a Miniaturized Predicativity

Stanley S. Wainer
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