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Notes on Forcing Axioms

Notes on Forcing Axioms

  • Author: Stevo Todorcevic
  • Publisher: World Scientific
  • ISBN: 9814571598
  • Category: Mathematics
  • Page: 236
  • View: 5115
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In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach–Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths. Contents:Baire Category Theorem and the Baire Category NumbersCoding Sets by the Real NumbersConsequences in Descriptive Set TheoryConsequences in Measure TheoryVariations on the Souslin HypothesisThe S-Spaces and the L-SpacesThe Side-condition MethodIdeal DichotomiesCoherent and Lipschitz TreesApplications to the S-Space Problem and the von Neumann ProblemBiorthogonal SystemsStructure of Compact SpacesRamsey Theory on OrdinalsFive Cofinal TypesFive Linear OrderingsCardinal Arithmetic and mmReflection PrinciplesAppendices:Basic NotionsPreserving Stationary SetsHistorical and Other Comments Readership: Graduate students and researchers in logic, set theory and related fields. Key Features:This is a first systematic exposition of the unified approach for building proper, semi-proper, and stationary preserving forcing notions through the method of using elementary submodels as side conditionsThe books starts from the classical applications of Martin's axioms and ends with some of the most sophisticated applications of the Proper Forcing Axioms. In this way, the reader is led into a natural process of understanding the combinatorics hidden behind the methodKeywords:Set Theory;Forcing Axioms

Slicing the Truth

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: 2008
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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

Combinatorial And Toric Homotopy: Introductory Lectures

Combinatorial And Toric Homotopy: Introductory Lectures

  • Author: Darby Alastair,Grbic Jelena,Lu Zhi
  • Publisher: World Scientific
  • ISBN: 9813226587
  • Category: Mathematics
  • Page: 448
  • View: 8334
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This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning

Forcing, Iterated Ultrapowers, and Turing Degrees

Forcing, Iterated Ultrapowers, and Turing Degrees

  • Author: Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin,Yue Yang
  • Publisher: World Scientific
  • ISBN: 9814699969
  • Category: Mathematics
  • Page: 184
  • View: 8273
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This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools. The major topics covered set theory and recursion theory, with particular emphasis on forcing, inner model theory and Turing degrees, offering a wide overview of ideas and techniques introduced in contemporary research in the field of mathematical logic. Contents:Prikry-Type Forcings and a Forcing with Short Extenders (Moti Gitik)The Turing Degrees: An Introduction (Richard A Shore)An Introduction to Iterated Ultrapowers (John Steel) Readership: Graduate students in mathematics, and researchers in logic, set theory and computability theory. Key Features:These are notes based on short courses given by three leading experts in set theory, recursion theory and their applicationsKeywords:Logic;Set Theory;Forcing;Recursion Theory;Computability Theory;Turing Degrees;C*-algebra

E-Recursion, Forcing and C*-Algebras

E-Recursion, Forcing and C*-Algebras

  • Author: Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin,Yue Yang
  • Publisher: World Scientific
  • ISBN: 9814602655
  • Category: Mathematics
  • Page: 228
  • View: 3876
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This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians. Contents:Selected Applications of Logic to Classification Problem for C*-Algebras (Ilijas Farah)Subcomplete Forcing and L-Forcing (Ronald Jensen)E-Recursion (Gerald E Sacks) Readership: Mathematics graduate students, researchers in logic, set theory and related areas. Key Features:These are notes based on short courses given by three leading experts in set theory, recursion theory and their applicationsKeywords:Logic;Set Theory;Forcing;E-recursion;C*-Algebra;Recursion Theory;Computability Theory

Computational Prospects of Infinity: Presented talks

Computational Prospects of Infinity: Presented talks

  • Author: Chi-Tat Chong
  • Publisher: World Scientific
  • ISBN: 9812796541
  • Category: Computers
  • Page: 420
  • View: 6753
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This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others.

Differentialgeometrie, Topologie und Physik

Differentialgeometrie, Topologie und Physik

  • Author: Mikio Nakahara
  • Publisher: Springer-Verlag
  • ISBN: 3662453002
  • Category: Science
  • Page: 597
  • View: 9395
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Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Konvexe Polyeder

Konvexe Polyeder

(originalens tit.: Vypuklye mnogogranniki)

  • Author: Aleksandr Danilovich Aleksandrov
  • Publisher: N.A
  • ISBN: N.A
  • Category: Polyhedra
  • Page: 419
  • View: 6831
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Die Grundlagen der Mathematik

Die Grundlagen der Mathematik

  • Author: David Hilbert
  • Publisher: Springer-Verlag
  • ISBN: 3663161021
  • Category: Mathematics
  • Page: 29
  • View: 6846
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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.

Einführung in die Funktionentheorie

Einführung in die Funktionentheorie

  • Author: R. Nevanlinna
  • Publisher: Springer-Verlag
  • ISBN: 3034840101
  • Category: Juvenile Nonfiction
  • Page: 388
  • View: 7025
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Poincarés Vermutung

Poincarés Vermutung

die Geschichte eines mathematischen Abenteuers

  • Author: Donal O'Shea
  • Publisher: N.A
  • ISBN: 9783596176632
  • Category:
  • Page: 376
  • View: 6447
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American Book Publishing Record

American Book Publishing Record

BPR cumulative

  • Author: Bowker Staff
  • Publisher: R. R. Bowker
  • ISBN: 9780835240857
  • Category: Reference
  • Page: 17426
  • View: 2341
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Meine Zahlen, meine Freunde

Meine Zahlen, meine Freunde

Glanzlichter der Zahlentheorie

  • Author: Paulo Ribenboim
  • Publisher: Springer-Verlag
  • ISBN: 3540879579
  • Category: Mathematics
  • Page: 391
  • View: 9347
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Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

Beweise und Widerlegungen

Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

  • Author: Imre Lakatos
  • Publisher: Springer-Verlag
  • ISBN: 3663001962
  • Category: Mathematics
  • Page: 163
  • View: 8386
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Georg Cantor

Georg Cantor

  • Author: Hans Joachim Ilgauds
  • Publisher: Springer-Verlag
  • ISBN: 3322822257
  • Category: Technology & Engineering
  • Page: 135
  • View: 9878
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Mathematische Berichterstattung in Hitlerdeutschland

Mathematische Berichterstattung in Hitlerdeutschland

der Niedergang des "Jahrbuchs über die Fortschritte der Mathematik"

  • Author: Reinhard Siegmund-Schultze
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 263
  • View: 7522
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Das Mathebuch

Das Mathebuch

Von Pythagoras bis in die 57. Dimension. 250 Meilensteine in der Geschichte der Mathematik

  • Author: Clifford A. Pickover
  • Publisher: N.A
  • ISBN: 9789089982803
  • Category:
  • Page: 527
  • View: 6522
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PISA Lernen für die Welt von morgen Erste Ergebnisse von PISA 2003

PISA Lernen für die Welt von morgen Erste Ergebnisse von PISA 2003

Erste Ergebnisse von PISA 2003

  • Author: OECD
  • Publisher: OECD Publishing
  • ISBN: 9789264063556
  • Category:
  • Page: 530
  • View: 1677
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Raum, Zeit, Materie

Raum, Zeit, Materie

  • Author: Hermann Weyl
  • Publisher: Рипол Классик
  • ISBN: 5880098028
  • Category: History
  • Page: N.A
  • View: 2786
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