Subsystems of Second Order Arithmetic

Author: Stephen George Simpson

Publisher: Cambridge University Press

ISBN: 052188439X

Category: Mathematics

Page: 444

View: 8437

This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Posted in Mathematics

Slicing the Truth

On the Computable and Reverse Mathematics of Combinatorial Principles

Author: Denis R Hirschfeldt

Publisher: World Scientific

ISBN: 9814612634

Category: Mathematics

Page: 232

View: 8167

This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics
Posted in Mathematics

Kurt Gödel

Essays for his Centennial

Author: Solomon Feferman,Charles Parsons,Stephen G. Simpson

Publisher: Cambridge University Press

ISBN: 1139487752

Category: Mathematics

Page: N.A

View: 7819

Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.
Posted in Mathematics

Effective Mathematics of the Uncountable

Author: Noam Greenberg,Denis Hirschfeldt,Joel David Hamkins,Russell Miller

Publisher: Cambridge University Press

ISBN: 1107014514

Category: Mathematics

Page: 204

View: 5552

A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Posted in Mathematics

The Bulletin of Symbolic Logic

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Electronic journals

Page: N.A

View: 3455

Posted in Electronic journals

Beweistheorie

Author: Kurt Schütte

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 355

View: 3888

Posted in Logic, Symbolic and mathematical

Grundlagen der Mathematik II

Author: David Hilbert,Paul Bernays

Publisher: Springer-Verlag

ISBN: 3642868967

Category: Mathematics

Page: 568

View: 8855

Der vorliegende Band schließt die Darstellung der Beweistheorie ab, die ich vor einigen Jahren zusammen mit P. BERNAYS begann. Auf meinen Wunsch hat P. BERNAYS wieder die Abfassung des Textes über nommen. Ich danke ihm für die Sorgfalt und Treue, mit der er meine Gedanken wiedergegeben hat, an deren Entwicklung er in jahrelanger Zusammenarbeit aufs stärkste beteiligt war. Ohne seine Mithilfe wäre die Vollendung dieses Buches unmöglich gewesen. Den Herren W. ACKERMANN, G. GENTZEN, A. SCHMIDT, H. SCHOLZ danke ich für ihre freundliche Mitwirkung bei den Korrekturen. Göttingen, im März 1939 HILBERT Zur Einführung Das vorliegende Buch soll einer eingehenden Orientierung über den gegenwärtigen Stoff der HILBERTschen Beweistheorie dienen. Wenn gleich das bisher hier Erreichte gemessen an den Zielen der Theorie sehr bescheiden ist, so liegt doch ein reichlicher Stoff an prägnanten Ergebnissen, an Gesichtspunkten und Beweisgedanken vor, die zur Kenntnis zu bringen als lohnend erscheint. Für die inhaltliche Gestaltung dieses zweiten Bandes waren durch den Zweck des Buches zwei Hauptthemata vorgezeichnet. - Es handelte sich einmal darum, die hauptsächlichen, an das e-Symbol sich knüpfenden beweistheoretischen Ansätze HILBERTS und ihre Durchführung zur ein gehenden Darstellung zu bringen.
Posted in Mathematics

Fundamentals of Mathematical Logic

Author: Peter G. Hinman

Publisher: A K Peters/CRC Press

ISBN: 9781568812625

Category: Mathematics

Page: 896

View: 1890

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Posted in Mathematics

Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 4941

Posted in Arithmetic

Die Grundlagen der Mathematik

Author: David Hilbert

Publisher: Springer-Verlag

ISBN: 3663161021

Category: Mathematics

Page: 29

View: 8366

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 1203

Posted in Logic, Symbolic and mathematical

Foundations of the Formal Sciences V

Infinite Games

Author: Stefan Bold,B Loewe,T Rasch

Publisher: N.A

ISBN: 9781904987758

Category: Computers

Page: 351

View: 504

Infinity can feature in games in various forms: we can play games of infinite length, with infinitely many players, or allow for infinitely many moves or strategies. Games of infinite length have been thoroughly investigated by mathematicians and have played a central role in mathematical logic. However, their applications go far beyond mathematics: they feature prominently in theoretical computer science, philosophical Gedankenexperiments, as limit cases in economical applications, and in many other applications. The conference Foundations of the Formal Sciences V focused on games of infinite length, but was very opn to include other notions of infinity in games as well.
Posted in Computers

Reverse mathematics 2001

Author: Stephen George Simpson

Publisher: A K Peters Ltd

ISBN: 9781568812632

Category: Mathematics

Page: 401

View: 7217

Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic.
Posted in Mathematics

Mengenlehre und ihre Logik

Author: Willard van Orman Quine

Publisher: Springer-Verlag

ISBN: 3322859436

Category: Mathematics

Page: 264

View: 3404

Posted in Mathematics

Axiomatische Wahrheitstheorien

Author: Volker Halbach

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3050072253

Category: Mathematics

Page: 257

View: 9291

Posted in Mathematics

Grundgesetze der Arithmetik

Author: Gottlob Frege

Publisher: Georg Olms Verlag

ISBN: 9783487098029

Category: Mathematics

Page: 265

View: 4500

Posted in Mathematics

Abriss der Logistik

Mit Besonderer Berücksichtigung der Relationstheorie und Ihrer Anwendungen

Author: Rudolf Carnap

Publisher: Springer

ISBN: 9783709131206

Category: Business & Economics

Page: 114

View: 3132

Posted in Business & Economics