Mathematical Logic: Edition 3
Heinz-Dieter Ebbinghaus · Jörg Flum · Wolfgang Thomas
may 2021 · Graduate Texts in Mathematics Libro 291 · Springer Nature
Libro electrónico
304
Páginas
reportLas calificaciones y opiniones no están verificadas. Más información
Acerca de este libro electrónico
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con sequence relation coincides with formal provability: By means of a calcu lus consisting of simple formal inference rules, one can obtain all conse quences of a given axiom system (and in particular, imitate all mathemat ical proofs). A short digression into model theory will help us to analyze the expres sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
Acerca del autor
Heinz-Dieter Ebbinghaus is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His work spans fields in logic, such as model theory and set theory, and includes historical aspects.
Jörg Flum is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His research interests include mathematical logic, finite model theory, and parameterized complexity theory.
Wolfgang Thomas is Professor Emeritus at the Computer Science Department of RWTH Aachen University. His research interests focus on logic in computer science, in particular logical aspects of automata theory.Califica este libro electrónico
Cuéntanos lo que piensas.
Información de lectura
Smartphones y tablets
Instala la app de Google Play Libros para Android y iPad/iPhone. Como se sincroniza de manera automática con tu cuenta, te permite leer en línea o sin conexión en cualquier lugar.
Laptops y computadoras
Para escuchar audiolibros adquiridos en Google Play, usa el navegador web de tu computadora.
Lectores electrónicos y otros dispositivos
Para leer en dispositivos de tinta electrónica, como los lectores de libros electrónicos Kobo, deberás descargar un archivo y transferirlo a tu dispositivo. Sigue las instrucciones detalladas que aparecen en el Centro de ayuda para transferir los archivos a lectores de libros electrónicos compatibles.
