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eBook details

• Title: Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles
• Author : Denis R. Hirschfeldt, Chitat Chong, Qi Feng & W Hugh Woodin Edited by Yue Yang
• Release Date : January 18, 2014
• Genre: Mathematics,Books,Science & Nature,Professional & Technical,
• Pages : * pages
• Size : 22808 KB

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.
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