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July 24 , 2007

Slicing the Truth

On the Computable and Reverse Mathematics of Combinatorial Principles


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.

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  • Setting Off: An Introduction
  • Gathering Our Tools: Basic Concepts and Notation
  • Finding Our Path: König'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

Readership: Graduates and researchers in mathematical logic.
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