Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles

Description

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

Get the book

Amazon.com

Search the book

eBay.com

Search the book

Similar books

• 

  Integral Geometry and Tomography: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, Held June 24-30, 1989, with Support from the...

  By Eric Grinberg, Eric Todd Quinto

  In Section 2 we will deal with the “discrete” case. Let S be a locally finite tree T endowed with the natural integer-valued distance function: the ...

• 

  Ordinary Differential Equations and Linear Algebra: A Systems Approach

  By Todd Kapitula

  ... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...

• 

  Cognition and Intractability: A Guide to Classical and Parameterized Complexity Analysis

  By Iris van Rooij, Mark Blokpoel, Johan Kwisthout

  x,y∈S δ(x,y) is maximum. u(x) + ADDITIVE SUBSET CHOICE Input: A set X = {x1 ,x2 ... F Tractability cycle Test 8.2 How (Not) to Deal with Intractability 173.

• 

  Mymathlab -- Standalone Access Card

  By Pearson Education, David P Pearson Education, Hall H Pearson Education

  Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable.

• 

  Mymathlab Student Acc Kit + Intro Alg Wrkshts

  By Inc. Pearson Education

  Mymathlab Student Acc Kit + Intro Alg Wrkshts

• 

  Pearson Mathematics 7: H.P

  By Pearson Education Australia Staff

  Pearson Mathematics homework program for Year 7 provides tear-out sheets which correspond with student book sections, providing systematic and cumulative skills revision of basic skills and current class topics in the form of take-home ...

• 

  Worksheets for Classroom Or Lab Practice for Intermediate Algebra: Graphs & Models

  By Addison-Wesley

  Worksheets for Classroom Or Lab Practice for Intermediate Algebra: Graphs & Models

• 

  Pearson Mathematics New South Wales 8 Student Book: Australian Curriculum

  By Pearson Education Australia Staff, Gael McLeod, David Coffey

  The Student Book provides an easy-to-use 'nuts and bolts' book at each year level.

• 

  Matrix Iterative Analysis

  By Richard S. Varga

  ... partial differential equations have received a great deal of attention. For excellent bibliographical coverage, see Todd (1956), Richtmyer (1957), ...

• 

  Mathematical Modelling: Education, Engineering and Economics - ICTMA 12

  By C Haines, P Galbraith, W Blum

  Todd, P. A., McKeen, .l. ... ANALYTICAL SUPPORT PROBLEM SOLVING Cognitive Perspectives on Modelling HOW DO STUDENTS AND TEACHERS DEAL Sodhi and Son 219 NOTE ...