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The Axiom Of Choice
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Book Synopsis The Axiom of Choice by : Thomas J. Jech
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Axiom of Choice written by Horst Herrlich and published by Springer. This book was released on 2006-07-21 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Zermelo’s Axiom of Choice by : G.H. Moore
Download or read book Zermelo’s Axiom of Choice written by G.H. Moore and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Consequences of the Axiom of Choice by : Paul Howard
Download or read book Consequences of the Axiom of Choice written by Paul Howard and published by American Mathematical Soc.. This book was released on 1998 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Equivalents of the Axiom of Choice by : Herman Rubin
Download or read book Equivalents of the Axiom of Choice written by Herman Rubin and published by Elsevier. This book was released on 1963 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Equivalents of the Axiom of Choice, II by : H. Rubin
Download or read book Equivalents of the Axiom of Choice, II written by H. Rubin and published by Elsevier. This book was released on 1985-03-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles.
Book Synopsis Freyd's Models for the Independence of the Axiom of Choice by : Andreas Blass
Download or read book Freyd's Models for the Independence of the Axiom of Choice written by Andreas Blass and published by American Mathematical Soc.. This book was released on 1989 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We relate Freyd's topos-theoretic models for the independence of the axiom of choice to the more familiar symmetric Boolean-valued models.
Book Synopsis Handbook of Analysis and Its Foundations by : Eric Schechter
Download or read book Handbook of Analysis and Its Foundations written by Eric Schechter and published by Academic Press. This book was released on 1996-10-24 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Book Synopsis Axiomatic Set Theory by : Patrick Suppes
Download or read book Axiomatic Set Theory written by Patrick Suppes and published by Courier Corporation. This book was released on 2012-05-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Book Synopsis Gödel's Theorems and Zermelo's Axioms by : Lorenz Halbeisen
Download or read book Gödel's Theorems and Zermelo's Axioms written by Lorenz Halbeisen and published by Springer Nature. This book was released on 2020-10-16 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Book Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski
Download or read book Set Theory for the Working Mathematician written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 1997-08-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Book Synopsis Principia Mathematica by : Alfred North Whitehead
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Set Theory and Its Philosophy by : Michael D. Potter
Download or read book Set Theory and Its Philosophy written by Michael D. Potter and published by Clarendon Press. This book was released on 2004 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
Book Synopsis People, Problems, and Proofs by : Richard J. Lipton
Download or read book People, Problems, and Proofs written by Richard J. Lipton and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.
Book Synopsis The Mathematics of Logic by : Richard W. Kaye
Download or read book The Mathematics of Logic written by Richard W. Kaye and published by Cambridge University Press. This book was released on 2007-07-12 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
Download or read book Naive Set Theory written by Paul Halmos and published by . This book was released on 2019-06 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org
Book Synopsis The Banach-Tarski Paradox by : Stan Wagon
Download or read book The Banach-Tarski Paradox written by Stan Wagon and published by Cambridge University Press. This book was released on 1993-09-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
