LEADER 04345nam 22005775 450 001 9910254060903321 005 20251116155104.0 010 $a3-319-29198-X 024 7 $a10.1007/978-3-319-29198-7 035 $a(CKB)3710000000667139 035 $a(EBL)4526302 035 $a(DE-He213)978-3-319-29198-7 035 $a(MiAaPQ)EBC4526302 035 $a(PPN)194077349 035 $a(EXLCZ)993710000000667139 100 $a20160504d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvances in proof theory /$fedited by Reinhard Kahle, Thomas Strahm, Thomas Studer 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016. 215 $a1 online resource (430 p.) 225 1 $aProgress in Computer Science and Applied Logic,$x2297-0576 ;$v28 300 $a"Advances in proof theory was the title of a symposium organized on the occasion of the 60th birthday of Gerhard J a? ger. The meeting took place on December 13 and 14, 2013, at the University of Bern, Switzerland." 311 08$a3-319-29196-3 320 $aIncludes bibliographical references at the end of each chapters. 327 $aW. 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. 330 $aThe aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium ?Advances in Proof Theory?, which was held in Bern in December 2013. Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science. . 410 0$aProgress in Computer Science and Applied Logic,$x2297-0576 ;$v28 606 $aLogic, Symbolic and mathematical 606 $aLogic 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aLogic$3https://scigraph.springernature.com/ontologies/product-market-codes/E16000 615 0$aLogic, Symbolic and mathematical. 615 0$aLogic. 615 14$aMathematical Logic and Foundations. 615 24$aLogic. 676 $a511.3 702 $aKahle$b Reinhard$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aStrahm$b Thomas$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aStuder$b Thomas$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254060903321 996 $aAdvances in proof theory$91523109 997 $aUNINA