Description

Book Synopsis

This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner.

Table of Contents

1. Introduction; 2. Systems of trees of strategies; 3. Σ1 constructions; 4. Δ2 constructions; 5. µ2 constructions; 6. Δ3 constructions; 7. Σ3 constructions; 8. Paths and links; 9. Backtracking; 10. Higher level constructions; 11. Infinite systems of trees.

A Framework for Priority Arguments 34 Lecture Notes in Logic Series Number 34

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    A Hardback by Manuel Lerman

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      Book details

      Publisher Cambridge University Press
      Published 19 April 2010
      ISBN-13 9780521119696
      978-0521119696
      ISBN-10 0521119693
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner.

      Table of Contents

      1. Introduction; 2. Systems of trees of strategies; 3. Σ1 constructions; 4. Δ2 constructions; 5. µ2 constructions; 6. Δ3 constructions; 7. Σ3 constructions; 8. Paths and links; 9. Backtracking; 10. Higher level constructions; 11. Infinite systems of trees.

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