Forcing For Mathematicians
Forcing For Mathematicians

Author: Nik Weaver

Publisher: World Scientific

Published: 2014-01-24

Total Pages: 153

ISBN-13: 9814566020

DOWNLOAD EBOOK

Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.

Combinatorial Set Theory
Combinatorial Set Theory

Author: Lorenz J. Halbeisen

Publisher: Springer

Published: 2017-12-20

Total Pages: 586

ISBN-13: 3319602314

DOWNLOAD EBOOK

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Set Theory and the Continuum Hypothesis
Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen

Publisher: Courier Corporation

Published: 2008-12-09

Total Pages: 196

ISBN-13: 0486469212

DOWNLOAD EBOOK

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Mathematics for Human Flourishing
Mathematics for Human Flourishing

Author: Francis Su

Publisher: Yale University Press

Published: 2020-01-07

Total Pages: 287

ISBN-13: 0300237138

DOWNLOAD EBOOK

"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

Author: W. Hugh Woodin

Publisher: Walter de Gruyter

Published: 2013-02-01

Total Pages: 944

ISBN-13: 3110804735

DOWNLOAD EBOOK

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

A Course in Mathematical Logic for Mathematicians
A Course in Mathematical Logic for Mathematicians

Author: Yu. I. Manin

Publisher: Springer Science & Business Media

Published: 2009-10-13

Total Pages: 389

ISBN-13: 1441906150

DOWNLOAD EBOOK

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.

Set Theory for the Working Mathematician
Set Theory for the Working Mathematician

Author: Krzysztof Ciesielski

Publisher: Cambridge University Press

Published: 1997-08-28

Total Pages: 256

ISBN-13: 9780521594653

DOWNLOAD EBOOK

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Multiple Forcing
Multiple Forcing

Author: Thomas J. Jech

Publisher: Cambridge University Press

Published: 1986

Total Pages: 148

ISBN-13: 0521266599

DOWNLOAD EBOOK

In this 1987 text Professor Jech gives a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though some results are also included, making the book attractive to set theorists and logicians.

Set Theory and the Continuum Problem
Set Theory and the Continuum Problem

Author: Raymond M. Smullyan

Publisher:

Published: 2010

Total Pages: 0

ISBN-13: 9780486474847

DOWNLOAD EBOOK

A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.