Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles

by Denis R Hirschfeldt, Chi Tat Chong, Qi Feng, Yue Yang, Theodore A Slaman

Overview

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.

Product Details

ISBN-13:	9789814612616
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/15/2014
Series:	Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore , #28
Pages:	232
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)

Table of Contents

Setting Off: An Introduction; Gathering Our Tools: Basic Concepts and Notation; Finding Our Path: Kö nig's Lemma and Computability; Gauging Our Strength: Reverse Mathematics; In Defense of Disarray; Achieving Consensus: Ramsey's Theorem; Preserving Our Power: Conservativity; Drawing a Map: Five Diagrams; Exploring Our Surroundings: The World Below RT22; Charging Ahead: Further Topics; Lagniappe: A Proof of Liu's Theorem