Includes bibliographical references (p. [135]) and index.

1 Syntax of First-Order Logic ................ .......... 1
1.1 First-Order Languages ............... ............... 1
1.2 Terms of a Language ............................... 4
1.3 Formulas of a Language ..................... ......... 6
1.4 First-Order Theories ............................... 10
2 Semantics of First-Order Languages ................... 15
2.1 Structures of First-Order Languages ................. . 16
2.2 Truth in a Structure ............................... 17
2.3 Model of a Theory ................................. 19
2.4 Embeddings and Isomorphisms ........................ 20
3 Propositional Logic ................ .................. 29
3.1 Syntax of Propositional Logic .......................... 30
3.2 Semantics of Propositional Logic ....................... 31
3.3 . Compactness Theorem for Propositional Logic ........... 33
3.4 Proof in Propositional Logic ........................... 37
3.5 Metatheorems in Propositional Logic. ................... 38
3.6 Post Tautology Theorem .............................. 42
4 Proof and Metatheorems in First-Order Logic .......... 45
4.1 Proof in First-Order Logic ......................... 45
4.2 Metatheorems in First-Order Logic ..................... 46
4.3 Some Metatheorems in Arithmetic ...................... 59
4.4 Consistency and Completeness ......................... 62
5 Completeness Theorem and Model Theory ............. 65
5.1 Completeness Theorem ............................. 65
5.2 Interpretations in a Theory ............................ 70
5.3 Extension by Definitions .............................. 72
5.4 Compactness Theorem and Applications. ................ 74
5.5 Complete Theories ................................. 77
5.6 Applications in Algebra .............................. 79
6 Recursive Functions and Arithmetization of Theories ... 83
6.1 Recursive Functions and Recursive Predicates ............ 84
6.2 Semirecursive Predicates .............................. 93
6.3 Arithmetization of Theories ........................... 96
6.4 Decidable Theories ................ ................ 103
7 Incompleteness Theorems and Recursion Theory ....... 107
7.1 Representability ..................................... 107
7.2 First Incompleteness Theorem ......................... 115
7.3 Arithmetical Sets ..................................... 116
7.4 Recursive Extensions of Peano Arithemetic .............. 125
7.5 Second Incompleteness Theorem ........................ 131