Predicative Arithmetic. (MN-32) :Predicative Arithmetic. (MN-32) ( Princeton Legacy Library )

Publication subTitle :Predicative Arithmetic. (MN-32)

Publication series :Princeton Legacy Library

Author: Nelson Edward;;;  

Publisher: Princeton University Press‎

Publication year: 2014

E-ISBN: 9781400858927

P-ISBN(Paperback): 9780691084558

Subject: O141.12 谓词演算(命题函项演算)

Keyword: 数学

Language: ENG

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Description

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Chapter

1. The Impredicativity of Induction

2. Logical Terminology

3. The Axioms of Arithmetic

4. Order

5. Induction by Relativization

6. Interpretability in Robinson's Theory

7. Bounded Induction

8. The Bounded Least Number Principle

9. The Euclidean Algorithm

10. Encoding

11. Bounded Separation and Minimum

12. Sets and Functions

13. Exponential Functions

14. Exponentiation

15. A Stronger Relativization Scheme

16. Bounds on Exponential Functions

17. Bounded Replacement

18. An Impassable Barrier

19. Sequences

20. Cardinality

21. Existence of Sets

22. Semibounded Replacement

23. Formulas

24. Proofs

25. Derived Rules of Inference

26. Special Constants

27. Extensions by Definition

28. Interpretations

29. The Arithmetization of Arithmetic

30. The Consistency Theorem

31. Is Exponentiation Total?

32. A Modified Hilbert Program

Bibliography

General Index

Index of Defining Axioms

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