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Reflexive Structures - An Introduction to Computability Theory (Paperback, Softcover reprint of the original 1st ed. 1988)
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Reflexive Structures - An Introduction to Computability Theory (Paperback, Softcover reprint of the original 1st ed. 1988)
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Reflexive Structures: An Introduction to Computability Theory is
concerned with the foundations of the theory of recursive
functions. The approach taken presents the fundamental structures
in a fairly general setting, but avoiding the introduction of
abstract axiomatic domains. Natural numbers and numerical functions
are considered exclusively, which results in a concrete theory
conceptually organized around Church's thesis. The book develops
the important structures in recursive function theory: closure
properties, reflexivity, enumeration, and hyperenumeration. Of
particular interest is the treatment of recursion, which is
considered from two different points of view: via the minimal fixed
point theory of continuous transformations, and via the well known
stack algorithm. Reflexive Structures is intended as an
introduction to the general theory of computability. It can be used
as a text or reference in senior undergraduate and first year
graduate level classes in computer science or mathematics.
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