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Beginner's Further Guide To Mathematical Logic, A (Hardcover)
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Beginner's Further Guide To Mathematical Logic, A (Hardcover)
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'A wealth of examples to which solutions are given permeate the
text so the reader will certainly be active.'The Mathematical
GazetteThis is the final book written by the late great puzzle
master and logician, Dr. Raymond Smullyan.This book is a sequel to
my Beginner's Guide to Mathematical Logic.The previous volume deals
with elements of propositional and first-order logic, contains a
bit on formal systems and recursion, and concludes with chapters on
Goedel's famous incompleteness theorem, along with related
results.The present volume begins with a bit more on propositional
and first-order logic, followed by what I would call a 'fein'
chapter, which simultaneously generalizes some results from
recursion theory, first-order arithmetic systems, and what I dub a
'decision machine.' Then come five chapters on formal systems,
recursion theory and metamathematical applications in a general
setting. The concluding five chapters are on the beautiful subject
of combinatory logic, which is not only intriguing in its own
right, but has important applications to computer science. Argonne
National Laboratory is especially involved in these applications,
and I am proud to say that its members have found use for some of
my results in combinatory logic.This book does not cover such
important subjects as set theory, model theory, proof theory, and
modern developments in recursion theory, but the reader, after
studying this volume, will be amply prepared for the study of these
more advanced topics.
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