Book:George S. Boolos/Computability and Logic/Third Edition

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



Source work progress
* : $1$ Enumerability


 * In-depth discussion about partial functions and enumerations which needs attention