Combinatorial Set Theory : With a Gentle Introduction to Forcing

Lorenz J. Halbeisen

ISBN 10: 1447121724 / ISBN 13: 9781447121725

Editore: Springer London, Springer London, 2011

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Druck auf Anfrage Neuware - Printed after ordering - This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field. Codice articolo 9781447121725

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Titolo: Combinatorial Set Theory : With a Gentle ...

Casa editrice: Springer London, Springer London

Data di pubblicazione: 2011

Legatura: Buch

Condizione: Neu

Descrizione articolo

Riassunto:

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Recensione:

From the reviews:

“The text is very well organised; each chapter ends with useful notes containing much historical background and the source of the main results, together with reports on related results and the references. The beautifully written book is intended for students on graduate courses in axiomatic set theory, and it is also excellent as a text for self-study.” (Peter Shiu, The Mathematical Gazette, Vol. 98 (541), March, 2014)

“The book under review provides a thorough and nicely written account of combinatorial set theory and infinite Ramsey theory together with a treatment of the underlying set theoretical axioms as well as of sophisticated methods which are involved in proving independence results. ... I can recommend this book to all graduate students, PostDocs, and researchers who are interested in set theoretical combinatorics ... . also mathematicians from other areas who are interested in the foundational aspects of their subject will enjoy this book.” (Ralf Schindler, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 115, 2013)

“This book provides a self-contained introduction to axiomatic set theory with main focus on infinitary combinatorics and the forcing technique. It is intended as a textbook in courses as well as for self-study. ... The author gives the historical background and the sources of the main results in the Notes of each chapter. He also gives hints for further studies in his sections ‘Related results’.” (Martin Weese, Zentralblatt MATH, Vol. 1237, 2012)