A Concise Introduction to Mathematical Logic - Brossura

Rautenberg, Wolfgang

Brossura

ISBN 10: 0387302948 ISBN 13: 9780387302942

Casa editrice: Springer Verlag, 2008

Riassunto

Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course.Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel's Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises.About the German edition:...The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created.- A.Nabebin, Zentralblatt

Su questo libro

Recensione:

From the reviews of the second edition:

"This is a translation of the author’s textbook (in German) on mathematical logic ... . The book’s goal is to provide three main theorems of mathematical logic ... . There are exercises. The book can be useful for students and for lecturers who prepare a mathematical logic course at a (technical) university." (Alex Nabebin, Zentralblatt MATH, Vol. 1093 (19), 2006)

Contenuti:

Foreword.- Preface.- Introduction.- Notation.- Propositional Logic.- Predicate Logic.- Gödel’s Completeness Theorem.- The Foundations of Logic Programming.- Elements of Model Theory.- Incompleteness and Undecidability.- On the Theory of Self-Reference.- Hints to the Exercises.- Literature.- Index of Terms and Names.- Index of Symbols.

Su questa edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2008
• ISBN 10: 0387302948
• ISBN 13: 9780387302942
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 256