Undecidable Theories: Studies in Logic and the Foundation of Mathematics (Dover Books on Mathematics) (Paperback)

Undecidable Theories: Studies in Logic and the Foundation of Mathematics (Dover Books on Mathematics) By Alfred Tarski, Andrzej Mostowski, Raphael M. Robinson Cover Image
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Description


This graduate-level book is well known for its proof that many mathematical systems--including lattice theory, abstract projective geometry, and closure algebras--are undecidable. Based on research conducted from 1938 to 1952, it consists of three treatises by a prolific author who ranks among the greatest logicians of all time.
The first article, A General Method in Proofs of Undecidability, examines theories with standard formalization, undecidable theories, interpretability, and relativization of quantifiers. The second feature, Undecidability and Essential Undecidability in Mathematics, explores definability in arbitrary theories and the formalized arithmetic of natural numbers. It also considers recursiveness, definability, and undecidability in subtheories of arithmetic as well as the extension of results to other arithmetical theories. The compilation concludes with "Undecidability of the Elementary Theory of Groups.

About the Author


Polish mathematician Alfred Tarski (1901-83) ranks among the greatest logicians of all time. Best known for his work on model theory, meta mathematics, and algebraic logic, he contributed to many other fields of mathematics and taught at the University of California, Berkeley, for more than 40 years.Tarski's student Andrzej Mostowksi worked at the University of Warsaw on first-order logic and model theory.Tarski's University of California colleague Raphael M. Robinson built on Tarski's concept of essential undecidability and proved a number of mathematical theories undecidable.


Product Details
ISBN: 9780486477039
ISBN-10: 0486477037
Publisher: Dover Publications
Publication Date: August 19th, 2010
Pages: 112
Language: English
Series: Dover Books on Mathematics