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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 Godel'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.

Category:

Science

Cover:

Paperback

Edition Number:

1

ISBN:

9789814725729

Pages:

277

Author:

Smullyan Raymond

Publisher:

WORLD SCIENTIFIC

Release Year:

2017

Raymond Smullyan, who has died aged 97, was a magician, concert pianist, hippie and Taoist; he was also an accomplished logician, mathematician and professor of Philosophy at Indiana University credited by the logician George Boolos as the originator of the “hardest logic puzzle ever”.

More on Propositional and First-Order Logic:

More on Propositional Logic

More on First-Order Logic

Recursion Theory and Metamathematics:

Some Special Topics

Elementary Formal Systems and Recursive Enumerability

Some Recursion Theory

Doubling Up

Metamathematical Applications

Elements of Combinatory Logic:

Beginning Combinatory Logic

Combinatorics Galore

Sages, Oracles and Doublets

Complete and Partial Systems

Combinators, Recursion and the Undecidable

Afterword: Where to Go From Here

References

Index