The Axiom Of Choice And Its Equivalent Forms
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The Axiom Of Choice And Its Equivalent Forms
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Author : Thomas Gerald McLenahan
language : en
Publisher:
Release Date : 1970
The Axiom Of Choice And Its Equivalent Forms written by Thomas Gerald McLenahan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Axiom of choice categories.
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 Mathematics 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.
Equivalents Of The Axiom Of Choice
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Author : Herman Rubin
language : en
Publisher: Elsevier
Release Date : 1963
Equivalents Of The Axiom Of Choice written by Herman Rubin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Axiom of choice categories.
Equivalents Of The Axiom Of Choice Ii
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Author : H. Rubin
language : en
Publisher: Elsevier
Release Date : 1985-03-01
Equivalents Of The Axiom Of Choice Ii written by H. Rubin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-03-01 with Mathematics categories.
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.
Equivalent Forms Of The Axiom Of Choice
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Author : Leon Francis Sagan
language : en
Publisher:
Release Date : 1964
Equivalent Forms Of The Axiom Of Choice written by Leon Francis Sagan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Axiom of choice categories.
Axiom Of Choice
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Author : Horst Herrlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Axiom Of Choice written by Horst Herrlich 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 2006-05-11 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.
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.
Some Equivalent Forms Of The Axiom Of Choice
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Author : Jack Dee Fisher
language : en
Publisher:
Release Date : 1966
Some Equivalent Forms Of The Axiom Of Choice written by Jack Dee Fisher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Axiom of choice categories.
Equivalent Forms Of The Axiom Of Choice
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Author : Pieter J. Helmke
language : en
Publisher:
Release Date : 1967
Equivalent Forms Of The Axiom Of Choice written by Pieter J. Helmke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
The Axiom Of Choice
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Author : Т Йех
language : en
Publisher: Courier Dover Publications
Release Date : 2008
The Axiom Of Choice written by Т Йех and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 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.