Discovering Modern Set Theory PDF Download
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Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 230 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821802666 |
Download Discovering Modern Set Theory. I: The Basics Book in PDF, ePub and Kindle
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821805282 |
Download Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician Book in PDF, ePub and Kindle
This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.
Author | : Winfried Just |
Publisher | : |
Total Pages | : |
Release | : 1996 |
Genre | : Set theory |
ISBN | : |
Download Discovering Modern Set Theory Book in PDF, ePub and Kindle
Author | : Winfried Just and Martin Weese |
Publisher | : American Mathematical Soc. |
Total Pages | : 244 |
Release | : |
Genre | : Set theory |
ISBN | : 9780821872086 |
Download Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician Book in PDF, ePub and Kindle
Author | : Ralf Schindler |
Publisher | : Springer |
Total Pages | : 332 |
Release | : 2014-05-22 |
Genre | : Mathematics |
ISBN | : 3319067257 |
Download Set Theory Book in PDF, ePub and Kindle
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Author | : Winfried Just |
Publisher | : |
Total Pages | : 224 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Discovering Modern Set Theory 2 Book in PDF, ePub and Kindle
Author | : Judith Roitman |
Publisher | : John Wiley & Sons |
Total Pages | : 188 |
Release | : 1990-01-16 |
Genre | : Mathematics |
ISBN | : 9780471635192 |
Download Introduction to Modern Set Theory Book in PDF, ePub and Kindle
This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Author | : Jeremy Gray |
Publisher | : Princeton University Press |
Total Pages | : 528 |
Release | : 2008-09-02 |
Genre | : Mathematics |
ISBN | : 1400829046 |
Download Plato's Ghost Book in PDF, ePub and Kindle
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 259 |
Release | : 2014-07-23 |
Genre | : Mathematics |
ISBN | : 0486497089 |
Download A Book of Set Theory Book in PDF, ePub and Kindle
"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"--
Author | : Loren Graham |
Publisher | : Harvard University Press |
Total Pages | : 252 |
Release | : 2009-03-31 |
Genre | : History |
ISBN | : 0674032934 |
Download Naming Infinity Book in PDF, ePub and Kindle
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.