Author | Smoryลski, Craig. author |
---|---|
Title | Logical Number Theory I [electronic resource] : An Introduction / by Craig Smoryลski |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991 |
Connect to | http://dx.doi.org/10.1007/978-3-642-75462-3 |
Descript | X, 405 p. 2 illus. online resource |
I. Arithmetic Encoding -- 1. Polynomials -- 2. Sums of Powers -- 3. The Cantor Pairing function -- 4. The Fueter-Pรณlya Theorem, I -- *5. The Fueter-Pรณlya 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 Coรซfficients -- *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