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.
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