نظریه‌های غیرقابل تصمیم‌گیری

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