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Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic
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Classical Recursion Theory, Volume II, Volume 143 (Hardcover)
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Classical Recursion Theory, Volume II, Volume 143 (Hardcover)
Series: Studies in Logic and the Foundations of Mathematics
Expected to ship within 12 - 19 working days
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Volume II of "Classical Recursion Theory" describes the universe
from a local (bottom-up
or synthetical) point of view, and covers the whole spectrum, from
the
recursive to the arithmetical sets.
The first half of the book provides a detailed picture of the
computable
sets from the perspective of Theoretical Computer Science. Besides
giving a
detailed description of the theories of abstract Complexity Theory
and of Inductive Inference, it contributes a uniform picture of the
most basic complexity
classes, ranging from small time and space bounds to the elementary
functions,
with a particular attention to polynomial time and space
computability. It also
deals with primitive recursive functions and larger classes, which
are of
interest to the proof theorist.
The second half of the book starts with the classical theory of
recursively
enumerable sets and degrees, which constitutes the core of
Recursion or
Computability Theory. Unlike other texts, usually confined to the
Turing
degrees, the book covers a variety of other strong reducibilities,
studying
both their individual structures and their mutual relationships.
The last
chapters extend the theory to limit sets and arithmetical sets. The
volume
ends with the first textbook treatment of the enumeration degrees,
which
admit a number of applications from algebra to the Lambda Calculus.
The book is a valuable source of information for anyone interested
in
Complexity and Computability Theory. The student will appreciate
the detailed
but informal account of a wide variety of basic topics, while the
specialist
will find a wealth of material sketched in exercises and asides. A
massive
bibliography of more than a thousand titles completes the treatment
on the
historical side.
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