This textbook is written for advanced undegraduates or first year graduate students of mathematics and computer science. It is also intended for the working mathematician who wants to gain an appreciation of Mathematical Logic. Thereare no prerequisites for this book; however, some mathematical maturity is required. The book is written in a totally mathematical style, and any mathematician should feel at home reading this. The book starts with the definition of first order languages, proceeds through propositional logic, completeness theorems, and finally the two Incompleteness Theorems of Godel. In the process, the reader is also introduced to model theory and recursion Theory. After reading this book, the reader will be ready to branch into model Theory, recursion Theory, axiomatic set theory or even theoretical computer science. Written in aclear, concise style. Contains numerous exercises and examples. Employs Godels completeness and incompleteness theorems to motivate the entire text. Modernlanguage and notation will appeal to undergrads as well as graduate students INDICE: Introduction.- First-order languages.- Semantics of first-order languages.- Propositional logic.- First-order theories.- Completeness theorem and model theory.- Recursive functions and arithmetization of theories.- Incompleteness theorems and recursion theory.- References.- Index.
- ISBN: 978-0-387-76275-3
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 160
- Fecha Publicación: 01/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés