Contributions to Mathematical Logic (eBook)

Front Cover 1
Contributions to Mathematical Logic 4
Copyright Page 5
Contents 6
CHAPTER 1. SATURATED INTUITIONISTIC THEORIES 14
Introduction 14
1. Preliminaries 15
2. Completeness Proof 16
3. Kripke Structures 18
4. Two Examples of Saturated Theories 20
5. Final Remarks 22
References 24
CHAPTER 2. DECISION PROBLEMS ABOUT ALGEBRAIC AND LOGICAL SYSTEMS AS A WHOLE AND RECURSIVELY ENUMERABLE DEGREES OF UNSOLVABILITY 26
1. Introduction 26
2. Statement of Results 28
3. Proofs of results 33
Supplement to Boone's "Algebraic Systems" 47
CHAPTER 3. ON RECURSIVELY UNSOLVABLE PROBLEMS IN TOPOLOGY AND THEIR CLASSIFICATION 50
0. Introduction Statement of Results
1. Logic 54
2. Algebra 59
3. Topology 64
References 85
CHAPTER 4. CONSTRUCTIVE THERMODYNAMICS 88
1. 88
2. 89
3. 91
4. 91
5. 93
6. 97
7. 101
Acknowledgements 102
References 102
CHAPTER 5. A DEDUCTION THEOREM FOR INFERENTIAL PREDICATE CALCULUS 104
1. Introduction 104
2. The Deduction Theorem 105
3. Extension to Modal Systems 108
4. Representation of the Outer System in the Inner 111
5. Theorems of Glivenko Type 113
References 120
CHAPTER 6. ZUR BERECHENBARKEIT PRIMITIV-REKURSIVER FUNKTIONALE ENDLICHER TYPEN 122
1. Ein Formales System . Von Termen Endlicher Typen 122
2. Regulare Terme 123
3. Eine Hierarchie Arithmetischer Operationen 126
4. Ersetzung Der Bar-Induktion Durch Transfinite Induktion 131
Literatur 133
CHAPTER 7. EQUATIONAL MAPS 134
1. A Review of Free Algebras 136
2. Algebraic Operations 141
3. Reducts 149
4. Equational and Functorial Maps 152
5. Construction of Equational Maps 157
6. Definable Maps and Syntactical Equivalences 163
Appendix 170
References 174
CHAPTER 9. SOME FORMS OF MODELS OF PROPORTIONAL CALCULI 176
1. Introduction 176
2. Models of Propositional Calculi 176
3. Modified S-Model 179
4. ms-Models and the Finite Model Property 185
References 187
CHAPTER 10. LENGTHS OF FORMULAS AND ELIMINATION OF QUANTIFIERS I 188
Introduction 188
1. 189
2. 189
3. 189
4. 190
5. 190
6. 191
7. 192
8. 193
9. 195
10. 197
11. 199
References 201
CHAPTER 11. A DECISION PROCEDURE FOR THE WEAK SECOND ORDER THEORY OF LINEAR ORDER 202
1. A Decidability Criterion 203
2. The Ws Theory of Linear Order 204
3. Proof of Theorem 1 205
4. Proof of Theorem 2 208
References 210
CHAPTER 12. STRUKTURZAHLEN IN ENDLICHEN RELATIONSSYSTEMEN 212
1. Ejnleitung 212
2. Anwendung Des Polyaschen Satzes Auf Das Anzahlproblem 213
3. Auswertung Der Polya-Formel Fur Reine Relationssysteme Mit U> s 1
4. Auswertung Der Polya-Formel Fur Reine Relationssysteme Mit U=s 1 221
Literatur 226
CHAPTER 13. A SURVEY OF SOME CONNECTIONS BETWEEN CLASSICAL INTUITIONISTIC AND MINIMAL LOGIC 244
1. Preliminaries 228
2. Interpretability 229
3. Theorems 231
4. Discussion 233
5. Proofs 235
References 241
CHAPTER 14. ZUR SEMANTIK DER INTUITIONISTISCHEN AUSSAGENLOGIK 244
CHAPTER 15. RECURSION THEORY AND THE THEOREM OF RAMSEY IN ONE-PLACE SECOND ORDER SUCCESSOR ARITHMETIC. 250
1. The System SC 251
2. Recursion Theory 253
3. The Theorem of Ramsey 257
References 267
CHAPTER 16. REFLECTION PRINCIPLES OF SUBSYSTEMS OF ANALYSIS 268
Chapter I 269
Chapter II 279
References 286
CHAPTER 17. EQUATIONAL LOGIC AND EQUATIONAL THEORIES OF 288
1. Algebras and Their Equational Theories 288
2. Finitely Based Theories 290
3. One-Based Theories 291
4. Independent Bases 295
5. Consistent and Complete Theories the Lattice of Equational Theories
6. Decision Problems 300
References 301
CHAPTER 18. THE USE OF "BROUWER'S PRINCIPLE" IN INTUITIONISTIC TOPOLOGY 302
1. Notations and Conventions 302
2. A Few Technicalities 303
3. Applications 305
References 311