A Framework for Priority Arguments: 34 (Lecture Notes in Logic, Series Number 34)

Manuel Lerman
Cambridge University Press, 4/19/2010
EAN 9780521119696, ISBN10: 0521119693

Hardcover, 192 pages, 23.6 x 15.7 x 1.5 cm
Language: English
Originally published in English

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.

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.