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Undecidable theories

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Author(s): Alfred Tarski; Andrzej Mostowski; Raphael M Robinson
Series: Studies in Logic and the Foundations of Mathematics 13
Publisher: Amsterdam, North-Holland Pub. Co.,
Year: 1971

Language: English
Pages: 108

Title ......Page 3
Copyright ......Page 4
Dedication ......Page 5
Preface ......Page 6
Contents ......Page 9
I. A GENERAL METHOD IN PROOFS OF UNDECIDABILITY. By ALFRED TARSKI ......Page 11
I.1. Introduction ......Page 13
I.2. Theories with standard formalization ......Page 15
I.3. Undecidable and essentially undecidable theories ......Page 22
I.4. Interpretability and weak interpretability ......Page 30
I.5. Relativization of quantifiers ......Page 34
I.6. Examples and applications ......Page 40
II. UNDECIDABILITY AND ESSENTIAL UNDECIDABILITY IN ARITHMETIC. By ANDRZEJ MOSTOWSKI, RAPHAEL M. ROBINSON, and ALFRED TARSKI ......Page 47
II.1. A summary of results; notation ......Page 49
II.2. Definability in arbitrary theories ......Page 54
II.3. Formalized arithmetic of natural numbers and its subtheories ......Page 61
II.4. Recursiveness and definability in subtheories of arithmetic ......Page 65
II.5. Undecidability of subtheories of arithmetic ......Page 70
II.6. Extension of the results to other arithmetical theories and to various theories of rings ......Page 75
III. UNDECIDABILITY OF THE ELEMENTARY THEORY OF GROUPS. By ALFRED TARSKI ......Page 85
Bibliography ......Page 99
Index ......Page 103