Equivalents Of The Axiom Of Choice Ii PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Equivalents Of The Axiom Of Choice Ii PDF full book. Access full book title Equivalents Of The Axiom Of Choice Ii.
Author | : H. Rubin |
Publisher | : Elsevier |
Total Pages | : 354 |
Release | : 1985-03-01 |
Genre | : Science |
ISBN | : 0080887651 |
Download Equivalents of the Axiom of Choice, II Book in PDF, ePub and Kindle
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.
Author | : Herman Rubin |
Publisher | : Elsevier |
Total Pages | : 159 |
Release | : 1963 |
Genre | : Axiom of choice |
ISBN | : 0444533990 |
Download Equivalents of the Axiom of Choice Book in PDF, ePub and Kindle
Author | : Horst Herrlich |
Publisher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2006-05-11 |
Genre | : Mathematics |
ISBN | : 3540309896 |
Download Axiom of Choice Book in PDF, ePub and Kindle
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.
Author | : Thomas J. Jech |
Publisher | : Courier Corporation |
Total Pages | : 226 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 0486466248 |
Download The Axiom of Choice Book in PDF, ePub and Kindle
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.
Author | : Paul Howard |
Publisher | : American Mathematical Soc. |
Total Pages | : 442 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821809776 |
Download Consequences of the Axiom of Choice Book in PDF, ePub and Kindle
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.
Author | : Michael Potter |
Publisher | : Clarendon Press |
Total Pages | : 362 |
Release | : 2004-01-15 |
Genre | : Philosophy |
ISBN | : 0191556432 |
Download Set Theory and its Philosophy Book in PDF, ePub and Kindle
Michael 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 | : Horst Herrlich |
Publisher | : Springer |
Total Pages | : 207 |
Release | : 2006-07-21 |
Genre | : Mathematics |
ISBN | : 3540342680 |
Download Axiom of Choice Book in PDF, ePub and Kindle
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.
Author | : G.H. Moore |
Publisher | : Springer Science & Business Media |
Total Pages | : 425 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461394783 |
Download Zermelo’s Axiom of Choice Book in PDF, ePub and Kindle
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.
Author | : Claire Ortiz Hill |
Publisher | : Open Court Publishing |
Total Pages | : 354 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780812694178 |
Download Husserl Or Frege? Book in PDF, ePub and Kindle
Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.
Author | : Lorenz J. Halbeisen |
Publisher | : Springer Science & Business Media |
Total Pages | : 449 |
Release | : 2011-11-24 |
Genre | : Mathematics |
ISBN | : 1447121732 |
Download Combinatorial Set Theory Book in PDF, ePub and Kindle
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.