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Author: Michael Holz
Publisher: Springer Science & Business Media
Published: 1999-09
Total Pages: 316
ISBN-13: 9783764361242
DOWNLOAD EBOOKAn introduction to modern cardinal arithmetic is presented in this volume, in addition to a survey of results. A discussion of classical theory is included, paired with investigations in pcf theory, which answers questions left open since the 1970’s.
Author: Michael Holz
Publisher: Springer Science & Business Media
Published: 2009-11-23
Total Pages: 309
ISBN-13: 3034603274
DOWNLOAD EBOOKThis book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.
Author: Lev D. Beklemishev
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 365
ISBN-13: 0080954863
DOWNLOAD EBOOKSet Theory
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
DOWNLOAD EBOOKAuthor: Michael Holz
Publisher: Birkhäuser
Published: 2010-04-06
Total Pages: 309
ISBN-13: 3034603304
DOWNLOAD EBOOKThis book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.
Author: Alfred Tarski
Publisher:
Published: 1949
Total Pages: 344
ISBN-13:
DOWNLOAD EBOOKAuthor: Saharon Shelah
Publisher: Oxford University Press on Demand
Published: 1994
Total Pages: 481
ISBN-13: 9780198537854
DOWNLOAD EBOOKIs the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence results of Godel and Cohen (and Easton) with some isolated positive results (likeGalvin-Hajnal). It was expected that only more independence results remained to be proved. The author has come to change his view. This enables us to get new results for the conventional cardinal arithmetic, thus supporting the interest in our view. We also find other applications, extend older methods of using normal fiters and prove the existence of Jonsson algebra.
Author: Joseph Breuer
Publisher: Courier Corporation
Published: 2012-08-09
Total Pages: 130
ISBN-13: 0486154874
DOWNLOAD EBOOKThis undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author: Michael Potter
Publisher: Clarendon Press
Published: 2004-01-15
Total Pages: 362
ISBN-13: 0191556432
DOWNLOAD EBOOKMichael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author: Kenneth E. Hummel
Publisher: CRC Press
Published: 2018-10-03
Total Pages: 345
ISBN-13: 1482285649
DOWNLOAD EBOOKBeyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.
