Topics In Set Theory
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Topics In Set Theory
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Author : Mohamed Bekkali
language : en
Publisher: Springer
Release Date : 2006-12-08
Topics In Set Theory written by Mohamed Bekkali and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
During the Fall Semester of 1987, Stevo Todorcevic gave a series of lectures at the University of Colorado. These notes of the course, taken by the author, give a novel and fast exposition of four chapters of Set Theory. The first two chapters are about the connection between large cardinals and Lebesque measure. The third is on forcing axioms such as Martin's axiom or the Proper Forcing Axiom. The fourth chapter looks at the method of minimal walks and p-functions and their applications. The book is addressed to researchers and graduate students interested in Set Theory, Set-Theoretic Topology and Measure Theory.
A Book Of Set Theory
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2014-07-23
A Book Of Set Theory written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Topics In Rough Set Theory
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Author : Seiki Akama
language : en
Publisher: Springer Nature
Release Date : 2019-09-10
Topics In Rough Set Theory written by Seiki Akama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Technology & Engineering categories.
This book discusses current topics in rough set theory. Since Pawlak’s rough set theory was first proposed to offer a basis for imprecise and uncertain data and reasoning from data, many workers have investigated its foundations and applications. Examining various topical issues, including object-oriented rough set models, recommendation systems, decision tables, and granular computing, the book is a valuable resource for students and researchers in the field.
An Outline Of Set Theory
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Author : James M. Henle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Outline Of Set Theory written by James M. Henle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.
Combinatorial Set Theory
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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer
Release Date : 2017-12-20
Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Mathematics categories.
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.
The Higher Infinite
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Author : Akihiro Kanamori
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-28
The Higher Infinite written by Akihiro Kanamori and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-28 with Mathematics categories.
Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.
Set Theory
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Author : Daniel W. Cunningham
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-18
Set Theory written by Daniel W. Cunningham and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-18 with Mathematics categories.
Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.
Set Theory For Physicists
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Author : Nicolas a Pereyra
language : en
Publisher: Morgan & Claypool
Release Date : 2019-05-10
Set Theory For Physicists written by Nicolas a Pereyra and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Science categories.
This book provides a rigorous, physics-focused introduction to set theory that is geared towards natural science majors. The science major is presented with a robust introduction to set theory, which concentrates on the specific knowledge and skills that will be needed for calculus and natural science topics in general.
Badiou S Being And Event And The Mathematics Of Set Theory
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Author : Burhanuddin Baki
language : en
Publisher: Bloomsbury Publishing
Release Date : 2015-01-15
Badiou S Being And Event And The Mathematics Of Set Theory written by Burhanuddin Baki and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-15 with Philosophy categories.
A valuable commentary of Badiou's use of mathematics in Being and Event, providing a new reading of his most important work.
Set Theory
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Author : Abhijit Dasgupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Set Theory written by Abhijit Dasgupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.