Book:George S. Boolos/Computability and Logic

Subject Matter

 * Mathematical Logic

Contents

 * Preface
 * Preface to the third edition
 * 1 Enumerability
 * 2 Diagonalization
 * 3 Turing machines
 * 4 Uncomputability via the busy beaver problem
 * 5 Uncomputability via diagonalization
 * 6 Abacus computable functions are Turing computable
 * 7 Recursive functions are abacus computable
 * 8 Turing computable functions are recursive
 * 9 First-order logic revisited
 * 10 First-order logic is undecidable
 * 11 First-order logic formalized: derivations and soundness
 * 12 Completeness of the formalization; compactness
 * 13 The Skolem-Löwenheim theorem
 * 14 Representability in $Q$
 * 15 Undecidability, undefinability and incompleteness
 * 16 Provability predicates and the unprovability of consistency
 * 17 Non-standard models of arithmetic
 * 18 Second-order logic
 * 19 On defining arithmetical truth
 * 20 Definability in arithmetic and forcing
 * 21 The decidability of arithmetic with addition, but not multiplication
 * 22 Dyadic logic is undecidable: eliminating names and function symbols
 * 23 The Craig interpolation lemma
 * 24 Two applications of Craig's lemma
 * 25 Monadic versus dyadic logic
 * 26 Ramsey's theorem
 * 27 Provability considered modal-logically
 * 28 Undecidable sentences
 * 29 Non-standard models of $Z$ are not recursive
 * Index