Advances in Proof Theory [electronic resource] / edited by Reinhard Kahle, Thomas Strahm, Thomas Studer.

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Series: Progress in Computer Science and Applied Logic ; 28Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016Description: XII, 425 p. 10 illus. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783319291987

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Printed edition:: No titleDDC classification:

511.3 23

LOC classification:

QA8.9-10.3

Online resources:

Click here to access online

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.

In: Springer eBooksSummary: 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. .

Item type:

eBooks

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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. .