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Undecidable Theories


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Table of Contents

I. A General Method in Proofs of Undecidability by Alfred Tarski I.1. Introduction I.2. Theories with standard formalization I.3. Undecidable and essentially undecidable theories I.4. Interpretability and weak interpretability I.5. Relativization of quantifiers I.6. Examples and applications II. Undecidability and Essential Undecidability in Arithmetic by Andrzej Mostowski, Raphael M. Robinson, and Alfred Tarski II.1. A summary of results; notation II.2. Definability in arbitrary theories II.3. Formalized arithmetic of natural numbers and its subtheories II.4. Recursiveness and definability in subtheories of arithmetic II.5. Undecidability of subtheories of arithmetic II.6. Extension of the results to other arithmetical theories and to various theories of rings III. Undecidability of the Elementary Theory of Groups by Alfred Tarski Bibliography Index

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.

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