Author(s): Yu. L. Ershov, E. A. Palyutin
Publisher: Mir Publishers
Year: 1984
Language: English
City: Moscow
Front Cover
Title page
CONTENTS
PREFACE
INTRODUCTION
Chapter 1 THE PROPOSITIONAL CALCULUS
1. SETS AND WORDS
Exercises
2. THE LANGUAGEOF THE PROPOSITIONAL CALCULUS
Exercises
3. AXIOM SYSTEM AND RULES OF INFERENCE
Exercises
4. THE EQUIVALENCE OF FORMULAS
Exercises
5. NORMAL FORMS
Exercises
6. SEMANTICSOF THE PROPOSITIONAL CALCULUS
Exercises
7. CHARACTERIZATION OF PROVABLE FORMULAS
Exercises
8. HILBERTIAN PROPOSITIONAL CALCULUS
Exercise
9. CONSERVATIVE EXTENSION OF CALCULI
Exercises
Chapter 2 SET THEORY
10. PREDICATES AND MAPPINGS
Exercises
11. PARTIALLY ORDERED SETS
Exercises
12. FILTERS OF BOOLEAN ALGEBRA
Exercises
13. THE POWER OF A SET
Exercises
14. THE AXIOM OF CHOICE
Exercise
Chapter 3 TRUTH ON ALGEBRAIC SYSTEMS
15. ALGEBRAIC SYSTEMS
Exercises
16. FORMULAS OF THE SIGNATURE $\Sigma$
Exercises
17. COMPACTNESS THEOREM
Exercises
Chapter 4 THE CALCULUS OF PREDICATES
18. AXIOMS AND RULES OF INFERENCE
Exercises
19. THE EQUIVALENCE OF FORMULAS
Exercises
20. NORMAL FORMS
Exercises
21. THEOREM ON THE EXISTENCE OF A MODEL
Exercises
22. HILBERTIAN CALCULUS OF PREDICATES
Exercises
23. PURE CALCULUS OF PREDICATES
Exercise
Chapter 5 MODEL THEORY
24. ELEMENTARY EQUIVALENCE
Exercises
25. AXIOMATIZABLE CLASSES
Exercises
26. SKOLEM FUNCTIONS
Exercise
27. MECHANISM OF COMPATIBILITY
Exercises
28. COUNTABLE HOMOGENEITY AND UNIVERSALITY
Exercises
29. CATEGORICITY
Exercises
Chapter 6 PROOF THEORY
30. THE GENTZEN SYSTEM G
Exercises
31. THE INVERTIBILITY OF RULES
Exercises
32. COMPARISON OF THE CALCULI CP$\Sigma$ AND G
Exercise
33. HERBRAND THEOREM
Chapter 7 ALGORITHMS AND RECURSIVE FUNCTIONS
35. NORMAL ALGORITHMS AND TURING MACHINES
Exercises
36. RECURSIVE FUNCTIONS
Exercises
37. RECURSIVELY ENUMERABLE PREDICATES
Exercises
38. UNDECIDABILITYOF THE CALCULUS OF PREDICATESAND GODEL'S INCOMPLETENESS THEOREM
Exercises
List of Symbols
Subject Index
