Mathematics Of Choice
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Mathematics Of Choice
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Author : Ivan Niven
language : en
Publisher: MAA
Release Date : 1965
Mathematics Of Choice written by Ivan Niven and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.
The Axiom Of Choice
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Author : Thomas J. Jech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
The Axiom Of Choice written by Thomas J. Jech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Axiom Of Choice
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Author : Horst Herrlich
language : en
Publisher: Springer
Release Date : 2006-07-21
Axiom Of Choice written by Horst Herrlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-21 with Mathematics categories.
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Mathematics Of Social Choice
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Author : Christoph Borgers
language : en
Publisher: SIAM
Release Date : 2010-01-01
Mathematics Of Social Choice written by Christoph Borgers and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Political Science categories.
Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.
Social Choice And The Mathematics Of Manipulation
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Author : Alan D. Taylor
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-09
Social Choice And The Mathematics Of Manipulation written by Alan D. Taylor 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 2005-05-09 with Business & Economics categories.
Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.
Consequences Of The Axiom Of Choice
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Author : Paul Howard
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Consequences Of The Axiom Of Choice written by Paul Howard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Axiom of choice categories.
This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number. Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography. Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row $n$, column $k$ gives the status of the implication ``form $n$ implies form $k$''. Software for easily extracting information from the table is also provided. Features: complete summary of all the work done in the last 100 years on statements that are weaker than the axiom of choice software provided gives complete, convenient access to information about relationships between the various consequences of the axiom of choice and about the models of set theory descriptions of more than 100 models used in the study of the axiom of choice an extensive bibliography About the software: Tables 1 and 2 are accessible on the PC-compatible software included with the book. In addition, the program maketex.c in the software package will create TeX files containing copies of Table 1 and Table 2 which may then be printed. (Tables 1 and 2 are also available at the authors' Web sites: http://www.math.purdue.edu/$\sim$jer/ or http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for setting up and using the software are included in the book's Introduction, and technical support is available directly from the authors.
Zermelo S Axiom Of Choice
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Author : G.H. Moore
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Zermelo S Axiom Of Choice written by G.H. Moore 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 grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.
The Axiom Of Choice
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Author : Thomas J. Jech
language : en
Publisher: Courier Corporation
Release Date : 2013-04-09
The Axiom Of Choice written by Thomas J. Jech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
The Axiom Of Choice
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Author : John Lane Bell
language : en
Publisher: Studies in Logic. Mathematical
Release Date : 2009
The Axiom Of Choice written by John Lane Bell and has been published by Studies in Logic. Mathematical this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book presents an overview of the development of the Axiom of Choice since its introduction by Zermelo at the beginning of the last century. The book surveys the Axiom of Choice from three perspectives. The first, or mathematical perspective, is that of the "working mathematician". This perspective brings into view the manifold applications of the Axiom of Choice-usually in the guise of Zorn s Lemma- in a great variety of areas of mathematics. The second, foundational, perspective is that of the logician or constructive mathematician concerned with the foundational status of the Axiom of Choice. The third, topos-theoretical, perspective is that taken by the mathematician or logician investigating the role of the Axiom of Choice in topos theory. Certain topics-for instance mathematical applications of the Axiom, and its relationship with logic-are discussed in considerable detail. Others-notably the consistency and independence of the Axiom of the usual systems of set theory-are given no more than summary treatment, the justification here being that these topics have been given full expositions elsewhere. It is hoped that the book will be of interest to logicians and mathematicians, both professional and prospective.
Individual Choice Behavior
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Author : R. Duncan Luce
language : en
Publisher: Courier Corporation
Release Date : 2012-06-22
Individual Choice Behavior written by R. Duncan Luce and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-22 with Mathematics categories.
This treatise presents a mathematical analysis of choice behavior. Starting with a general axiom, it then examines applications of the theory to substantive problems: psychophysics, utility, and learning. 1959 edition.