Logical Number Theory I

The 2-volume introductory textbook on logical number theory - or, number theory as studied by the logician - consists of this first volume that can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, and a second volume to follow soon with more sophisticated content and treatment but still accessible to students having read volume I or had a standard introductory course. The author is well known beyond his own field of specialisation for his expository talent and his lucid and enjoyable writing style.

Inhalt
I. Arithmetic Encoding.- 1. Polynomials.- 2. Sums of Powers.- 3. The Cantor Pairing function.- 4. The Fueter-Pólya Theorem, I.- *5. The Fueter-Pólya Theorem, II.- 6. The Chinese Remainder Theorem.- 7. The ?-Function and Other Encoding Schemes.- 8. Primitive Recursion.- *9. Ackermann Functions.- 10. Arithmetic Relations.- 11. Computability.- 12. Elementary Recursion Theory.- 13. The Arithmetic Hierarchy.- 14. Reading List.- II. Diophantine Encoding.- 1. Diophantine Equations; Some Background.- 2. Initial Results; The Davis-Putnam-Robinson Theorem.- 3. The Pell Equation, I.- 4. The Pell Equation, II.- 5. The Diophantine Nature of R.E. Relations.- 6. Applications.- 7. Forms.- *8. Binomial Coëfficients.- *9. A Direct Proof of the Davis-Putnam-Robinson Theorem.- *10. The 3-Variable Exponential Diophantine Result.- 11. Reading List.- III. Weak Formal Theories of Arithmetic.- 1. Ignorabimus?.- 2. Formal Language and Logic.- 3. The Completeness Theorem.- 4. Presburger-Skolem Arithmetic; The Theory of Addition.- *5. Skolem Arithmetic; The Theory of Multiplication.- 6. Theories with + and ?; Incompleteness and Undecidability.- 7. Semi-Repiesentability of Functions.- 8. Further Undecidability Results.- 9. Reading List.- Index of Names.- Index of Subjects.