Predicative Arithmetic

*FrontMatter, pg. i*Acknowledgments, pg. v*Table of Contents, pg. vii*Chapter 1. The impredicativity of induction, pg. 1*Chapter 2. Logical terminology, pg. 3*Chapter 3. The axioms of arithmetic, pg. 8*Chapter 4. Order, pg. 10*Chapter 5. Induction by relativization, pg. 12*Chapter 6. Interpretability in Robinson's theory, pg. 16*Chapter 7. Bounded induction, pg. 23*Chapter 8. The bounded least number principle, pg. 29*Chapter 9. The euclidean algorithm, pg. 32*Chapter 10. Encoding, pg. 36*Chapter 11. Bounded separation and minimum, pg. 43*Chapter 12. Sets and functions, pg. 46*Chapter 13. Exponential functions, pg. 51*Chapter 14. Exponentiation, pg. 54*Chapter 15. A stronger relativization scheme, pg. 60*Chapter 16. Bounds on exponential functions, pg. 64*Chapter 17. Bounded replacement, pg. 70*Chapter 18. An impassable barrier, pg. 73*Chapter 19. Sequences, pg. 82*Chapter 20. Cardinality, pg. 90*Chapter 21. Existence of sets, pg. 95*Chapter 22. Semibounded Replacement, pg. 98*Chapter 23. Formulas, pg. 101*Chapter 24. Proofs, pg. 111*Chapter 25. Derived rules of inference, pg. 115*Chapter 26. Special constants, pg. 134*Chapter 27. Extensions by definition, pg. 136*Chapter 28. Interpretations, pg. 152*Chapter 29. The arithmetization of arithmetic, pg. 157*Chapter 30. The consistency theorem, pg. 162*Chapter 31. Is exponentiation total?, pg. 173*Chapter 32. A modified Hilbert program, pg. 178*Bibliography, pg. 181*General index, pg. 183*Index of defining axioms, pg. 186