A Course on Mathematical Logic

Shashi Mohan Srivastava

ISBN 10: 1461457459 / ISBN 13: 9781461457459

Verlag: Springer US, Springer New York, 2013

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel's incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is toprovide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Bestandsnummer des Verkäufers 9781461457459

Bibliografische Details

• Titel: A Course on Mathematical Logic
• Verlag: Springer US, Springer New York
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 1461457459
• ISBN-13: 9781461457459
• Einband: Taschenbuch
• Auflage: 2. Auflage
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability.

In this new edition, many small and large changes have been made throughout the text.  The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic.  Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry.  Some proofs, such as the proof of the very important completeness theorem,  have been completely rewritten in a more clear and concise manner.  The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Über die Autorin bzw. den Autor

Shashi Mohan Srivastava is a professor at the Indian Statistical Institute, Kolkata, India. He is also the author of A Course on Borel Sets (GTM 180), and recipient of the Indian National Science Academy Medal for Young Scientists in 1981.