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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.
PART I. ELEMENTARY MATHEMATICAL LOGIC


CHAPTER I. THE PROPOSITIONAL CALCULUS  
1. Linguistic considerations: formulas  
2. "Model theory: truth tables,validity "  
3. "Model theory: the substitution rule, a collection of valid formulas"  
4. Model theory: implication and equivalence  
5. Model theory: chains of equivalences  
6. Model theory: duality  
7. Model theory: valid consequence  
8. Model theory: condensed truth tables  
9. Proof theory: provability and deducibility  
10. Proof theory: the deduction theorem  
11. "Proof theory: consistency, introduction and elimination rules"  
12. Proof theory: completeness  
13. Proof theory: use of derived rules  
14. Applications to ordinary language: analysis of arguments  
15. Applications to ordinary language: incompletely stated arguments  
CHAPTER II. THE PREDICATE CALCULUS  
16. "Linguistic considerations: formulas, free and bound occurrences of variables"  
17. "Model theory: domains, validity"  
18. Model theory: basic results on validity  
19. Model theory: further results on validity  
20. Model theory: valid consequence  
21. Proof theory: provability and deducibility  
22. Proof theory: the deduction theorem  
23. "Proof theory: consistency, introduction and elimination rules"  
24. "Proof theory: replacement, chains of equivalences"  
25. "Proof theory: alterations of quantifiers, prenex form"  
26. "Applications to ordinary language: sets, Aristotelian categorical forms"  
27. Applications to ordinary language: more on translating words into symbols  
CHAPTER III. THE PREDICATE CALCULUS WITH EQUALITY  
28. "Functions, terms"  
29. Equality  
30. "Equality vs. equivalence, extensionality"  
31. Descriptions  
PART II. MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMATICS  
CHAPTER IV. THE FOUNDATIONS OF MATHEMATICS  
32. Countable sets  
33. Cantor's diagonal method  
34. Abstract sets  
35. The paradoxes  
36. Axiomatic thinking vs. intuitive thinking in mathematics  
37. "Formal systems, metamathematics"  
38. Formal number theory  
39. Some other formal systems  
CHAPTER V. COMPUTABILITY AND DECIDABILITY  
40. Decision and computation procedures  
41. "Turing machines, Church's thesis"  
42. Church's theorem (via Turing machines)  
43. Applications to formal number theory: undecidability (Church) and incompleteness (Gödel's theorem)  
44. Applications to formal number theory: consistency proofs (Gödel's second theorem)  
45. "Application to the predicate calculus (Church, Turing)"  
46. "Degrees of unsolvability (Post), hierarchies (Kleene, Mostowski)."  
47. Undecidability and incompleteness using only simple consistency (Rosser)  
CHAPTER VI. THE PREDICATE CALCULUS (ADDITIONAL TOPICS)  
48. Gödel's completeness theorem: introduction  
49. Gödel's completeness theorem: the basic discovery  
50. "Gödel's completeness theorem with a Gentzentype formal system, the LöwenheimSkolem theorem"  
51. Gödel's completeness theorem (with a Hilberttype formal system)  
52. "Gödel's completeness theorem, and the LöwenheimSkolem theorem, in the predicate calculus with equality"  
53. Skolen's paradox and nonstandard models of arithmetic  
54. Gentzen's theorem  
55. "Permutability, Herbrand's theorem"  
56. Craig's interpolation theorem  
57. "Beth's theorem on definability, Robinson's consistency theorem"  
BIBLIOGRAPHY  
THEOREM AND LEMMA NUMBERS: PAGES  
LIST OF POSTULATES  
SYMBOLS AND NOTATIONS  
INDEX  