Combinatorial Set Theory

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Combinatorial Set Theory

Lorenz J. Halbeisen
Combinatorial Set Theory Book PDF

Author : Lorenz J. Halbeisen
Publisher : Springer
Page : 594 pages
File Size : 45,7 Mb
Release : 2017-12-20
Category : Mathematics
ISBN : 9783319602318

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

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.

Combinatorial Set Theory of C*-algebras

Ilijas Farah
Combinatorial Set Theory of C algebras Book PDF

Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 42,9 Mb
Release : 2019-12-24
Category : Mathematics
ISBN : 9783030270933

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Combinatorial Set Theory of C*-algebras by Ilijas Farah Pdf

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Combinatorial Set Theory: Partition Relations for Cardinals

P. Erdös,A. Máté,A. Hajnal,P. Rado
Combinatorial Set Theory Partition Relations for Cardinals Book PDF

Author : P. Erdös,A. Máté,A. Hajnal,P. Rado
Publisher : Elsevier
Page : 349 pages
File Size : 41,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 9780444537454

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Combinatorial Set Theory: Partition Relations for Cardinals by P. Erdös,A. Máté,A. Hajnal,P. Rado Pdf

This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.

Combinatorial Set Theory

Lorenz J. Halbeisen
Combinatorial Set Theory Book PDF

Author : Lorenz J. Halbeisen
Publisher : Springer
Page : 456 pages
File Size : 49,9 Mb
Release : 2011-12-01
Category : Mathematics
ISBN : 1447121740

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

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.

Surveys in Set Theory

A. R. D. Mathias
Surveys in Set Theory Book PDF

Author : A. R. D. Mathias
Publisher : Cambridge University Press
Page : 257 pages
File Size : 40,7 Mb
Release : 1983-10-13
Category : Mathematics
ISBN : 9780521277334

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Surveys in Set Theory by A. R. D. Mathias Pdf

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Extremal Finite Set Theory

Daniel Gerbner,Balazs Patkos
Extremal Finite Set Theory Book PDF

Author : Daniel Gerbner,Balazs Patkos
Publisher : CRC Press
Page : 269 pages
File Size : 44,8 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9780429804113

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Extremal Finite Set Theory by Daniel Gerbner,Balazs Patkos Pdf

Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.

Problems and Theorems in Classical Set Theory

Peter Komjath,Vilmos Totik
Problems and Theorems in Classical Set Theory Book PDF

Author : Peter Komjath,Vilmos Totik
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 40,8 Mb
Release : 2006-11-22
Category : Mathematics
ISBN : 9780387362199

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Problems and Theorems in Classical Set Theory by Peter Komjath,Vilmos Totik Pdf

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Combinatorics

Béla Bollobás
Combinatorics Book PDF

Author : Béla Bollobás
Publisher : Cambridge University Press
Page : 196 pages
File Size : 46,9 Mb
Release : 1986-07-31
Category : Mathematics
ISBN : 0521337038

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Combinatorics by Béla Bollobás Pdf

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

Classical Topology and Combinatorial Group Theory

John Stillwell
Classical Topology and Combinatorial Group Theory Book PDF

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243724

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Classical Topology and Combinatorial Group Theory by John Stillwell Pdf

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Set Theory

Andras Hajnal,Peter Hamburger
Set Theory Book PDF

Author : Andras Hajnal,Peter Hamburger
Publisher : Cambridge University Press
Page : 332 pages
File Size : 44,6 Mb
Release : 1999-11-11
Category : Mathematics
ISBN : 052159667X

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Set Theory by Andras Hajnal,Peter Hamburger Pdf

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

Applications of Group Theory to Combinatorics

Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Applications of Group Theory to Combinatorics Book PDF

Author : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 46,8 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765

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Applications of Group Theory to Combinatorics by Jack Koolen,Jin Ho Kwak,Ming-Yao Xu Pdf

Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state

Combinatorics and Graph Theory

John Harris,Jeffry L. Hirst,Michael Mossinghoff
Combinatorics and Graph Theory Book PDF

Author : John Harris,Jeffry L. Hirst,Michael Mossinghoff
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 54,5 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387797113

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Combinatorics and Graph Theory by John Harris,Jeffry L. Hirst,Michael Mossinghoff Pdf

These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Set Theory

A. Hajnal,P. Hamburg
Set Theory Book PDF

Author : A. Hajnal,P. Hamburg
Publisher : Unknown
Page : 325 pages
File Size : 44,9 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362555

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Set Theory by A. Hajnal,P. Hamburg Pdf

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

Handbook of Set Theory

Matthew Foreman,Akihiro Kanamori
Handbook of Set Theory Book PDF

Author : Matthew Foreman,Akihiro Kanamori
Publisher : Springer Science & Business Media
Page : 2230 pages
File Size : 53,5 Mb
Release : 2009-12-10
Category : Mathematics
ISBN : 9781402057649

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Handbook of Set Theory by Matthew Foreman,Akihiro Kanamori Pdf

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

A Course in Combinatorics

J. H. van Lint,Richard Michael Wilson
A Course in Combinatorics Book PDF

Author : J. H. van Lint,Richard Michael Wilson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 47,9 Mb
Release : 2001-11-22
Category : Mathematics
ISBN : 0521006015

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A Course in Combinatorics by J. H. van Lint,Richard Michael Wilson Pdf

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.