Overview

This study analyzes number theory as studied by the logician. It is the first volume of a two-volume introduction to mathematical logic, which deals with recursion theory, first-order logic, completeness, incompleteness and undecidability. It contains a logical discussion of diophantine decision problems and logico-arithmetical matters. Each chapter contains exercises and historical comments designed to develop the student's perspective of the subject.

Full Product Details

Author:   Craig Smorynski
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1991
Dimensions:   Width: 17.00cm , Height: 2.20cm , Length: 24.20cm
Weight:   0.715kg
ISBN:  

9783540522362

ISBN 10:   3540522360
Pages:   405
Publication Date:   25 April 1991
Audience:   College/higher education ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I. Arithmetic Encoding.- 1. Polynomials.- 2. Sums of Powers.- 3. The Cantor Pairing function.- 4. The Fueter-Polya Theorem, I.- *5. The Fueter-Polya 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 Coefficients.- *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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions