Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

Description

People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important results in the study of a first order theory of the natural numbers, called Peano arithmetic and its fragments (subtheories). The field is quite active, but only a small part of the results has been covered in monographs. This book is divided into three parts. In Part A, the authors develop parts of mathematics and logic in various fragments. Part B is devoted to incompleteness. Part C studies systems that have the induction schema restricted to bounded formulas (Bounded Arithmetic). One highlight of this section is the relation of provability to computational complexity. The study of formal systems for arithmetic is a prerequisite for understanding results such as Gödel's theorems. This book is intended for those who want to learn more about such systems and who want to follow current research in the field. The book contains a bibliography of approximately 1000 items.

Disclaimer:
Contents of this page are indexed from the Internet. All actions are under your responsability. Email us to report illegal contents or external links and we'll remove them immediately.

Please check the description for download links if any or do a search to find alternative books.

Can't Download?
Please search mirrors if you can't find download links for "Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)" in "Description" and someone else may update the links. Check the comments when back to find any updates.

Search Mirrors
Maybe some mirror pages will be helpful, search this book at top of this page or click here to find more info.

1. Ebooks list page : 2603
2. Subsystems of Second Order Arithmetic (Perspectives in Logic)
3. Recursion Theory for Metamathematics (Oxford Logic Guides)
4. Constructibility (Perspectives in Mathematical Logic)
5. Essential Stability Theory (Perspectives in Mathematical Logic)
6. Fundamentals of Stability Theory (Perspectives in Mathematical Logic)
7. Higher Recursion Theory (Perspectives in Mathematical Logic)
8. Computability in Analysis and Physics (Perspectives in Mathematical Logic)
9. General Recursion Theory: An Axiomatic Approach (Perspectives in Mathematical Logic)
10. Degrees of Unsolvability: Local and Global Theory (Perspectives in Mathematical Logic)
11. Arithmetic and Logic in Computer Systems
12. Arithmetic.and.Logic.in.Computer.Systems
13. Arithmetic and Logic in Computer Systems
14. Arithmetic and Logic in Computer Systems
15. Cardinal Arithmetic (Oxford Logic Guides)
16. Arithmetic Duality Theorems (Perspectives in Mathematics, Vol. 1)