Logical Number Theory I
An Introduction
Published on 25. April 1991
Book
Paperback/Softback
X, 405 pages
978-3-540-52236-2 (ISBN)
Description
Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1991
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Lower undergraduate
Illustrations
2 s/w Abbildungen
X, 405 p. 2 illus.
Dimensions
Height: 242 mm
Width: 170 mm
Thickness: 23 mm
Weight
715 gr
ISBN-13
978-3-540-52236-2 (9783540522362)
DOI
10.1007/978-3-642-75462-3
Schweitzer Classification
Person
Content
I. Arithmetic Encoding.- 1. Polynomials.- 2. Sums of Powers.- 3. The Cantor Pairing function.- 4. The Fueter-Pólya Theorem, I.- *5. The Fueter-Pólya 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 Coëfficients.- *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.