A Framework for Priority Arguments

Erscheinungsjahr 2010
ISBN: 978-0-521-11969-6
Verlag: Cambridge University Press

Buch, Englisch, Band 34, 192 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 440 g

Reihe: Lecture Notes in Logic

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.

Autoren/Hrsg.

Lerman, Manuel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten

Inhaltsverzeichnis

1. Introduction; 2. Systems of trees of strategies; 3. S1 constructions; 4. ?2 constructions; 5. µ2 constructions; 6. ?3 constructions; 7. S3 constructions; 8. Paths and links; 9. Backtracking; 10. Higher level constructions; 11. Infinite systems of trees.

Über Autor(innen)

Lerman, Manuel
Manuel Lerman is a Professor Emeritus of the Department of Mathematics at the University of Connecticut. He is the author of Degrees of Unsolvability: Local and Global Theory, has been the managing editor for the book series Perspectives in Mathematical Logic, has been an editor of Bulletin for Symbolic Logic, and is an editor of the ASL's Lecture Notes in Logic series.