CHAPTER ZERO Useful Facts about Sets　1 CHAPTER ONE Sentential Logic　11 1.0　Informal Remarks on Formal Languages　11 1.1　The Language of Sentential Logic　13 1.2　Truth Assignments　20 1.3　A Parsing Algorithm　29 1.4　Induction and Recursion　34 1.5　Sentential Connectives　45 1.6　Switching Circuits　54 1.7　Compactness and Effectiveness　59 CHAPTER TWO　First-Order Logic　67 2.0　Preliminary Remarks　67 2. l　First-Order Languages　69 2.2　Truth and Models　80 2.3　A Parsing Algorithm　105 2.4　A Deductive Calculus　109 2.5　Soundness and Completeness Theorems　131 2.6　Models of Theories　147 2.7　Interpretations Between Theories　164 2.8　Nonstandard Analysis　173 CHAPTER THREE　Undecidability　182 3.0　Number Theory　182 3.1　Natural Numbers with Successor　187 3.2　Other Reducts of Number Theory　193 3.3　A Subtheory of Number Theory　202 3.4　Arithmetization of Syntax　224 3.5　Incompleteness and Undecidability　234 3.6　Recursive Functions　247 3.7　Second Incompleteness Theorem　266 3.8　Representing Exponentiation　276 CHAPTER FOUR　Second-Order Logic　282 4.1　Second-Order Languages　282 4.2　Skolem Functions　287 4.3　Many-Sorted Logic　295 4.4　General Structures　299 SUGGESTIONS FOR FURTHER READING　307 LIST OF SYMBOLS　309 INDEX