This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography. – Contents ; – 1. Formal Systems; – 2. Propositional calculi; – 3. Predicate calculi; – 4. A complete, decidable arithmetic. The system Aoo; – 5. Aoo-Definable functions; – 6. A complete, undecidable arithmetic. The system Ao; – 7. Ao-Definable functions. Recursive function theory; – 8. An incomplete undecidable arithmetic. The system A; – 9. A-Definable sets of lattice points; – 10. Induction; – 11. Extensions of the system A1; – 12. Models. – Epilogue; – Glossary of special symbols; – Note on references; – References; – Index.