Set Theory

Author: Thomas Jech
Publisher: Springer Science & Business Media
ISBN: 9783540447610
Release Date: 2007-05-23
Genre: Mathematics

This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present ‘Third Millennium’ edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS

Combinatorial Set Theory

Author: Lorenz J. Halbeisen
Publisher: Springer Science & Business Media
ISBN: 1447121732
Release Date: 2011-11-24
Genre: Mathematics

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.

A Course on Set Theory

Author: Ernest Schimmerling
Publisher: Cambridge University Press
ISBN: 9781139501484
Release Date: 2011-07-28
Genre: Mathematics

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.

A Course in Mathematical Logic for Mathematicians

Author: Yu. I. Manin
Publisher: Springer Science & Business Media
ISBN: 9781441906151
Release Date: 2009-10-13
Genre: Mathematics

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

Newsletter

Author: New Zealand Mathematical Society
Publisher:
ISBN: UOM:39015060913897
Release Date: 2004
Genre: Mathematics


Measures in Mice

Author: Farmer Salamander Schlutzenberg
Publisher:
ISBN: UCAL:C3510340
Release Date: 2007
Genre:


Forthcoming Books

Author: Rose Arny
Publisher:
ISBN: UOM:39015058394233
Release Date: 2001
Genre: American literature


Author:
Publisher:
ISBN: UOM:39015080215554
Release Date: 1974
Genre: Catalogs, Union


Books in Print

Author:
Publisher:
ISBN: UOM:39015054048460
Release Date: 2004
Genre: American literature

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.