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Lecture Notes in Mathematics Ser.: Axiom of Choice by Horst Herrlich (2006, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540309896
ISBN-139783540309895
eBay Product ID (ePID)52636858
Product Key Features
Number of PagesXiv, 198 Pages
Publication NameAxiom of Choice
LanguageEnglish
SubjectAlgebra / Abstract, Functional Analysis, General, Logic
Publication Year2006
TypeTextbook
AuthorHorst Herrlich
Subject AreaMathematics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight24.3 Oz
Item Length9.2 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2006-921740
ReviewsFrom the reviews:"The book is an excellent introduction to the Axiom of Choice, its consequences and even its possible replacements. Although the author claims not to have written a textbook, compendium or history, the book might be used as any of these three. … there are many diagrams throughout the text and in the appendix detailing the relationships between the Axiom of Choice and its consequences. It certainly fulfills its stated purpose of whetting the reader's appetite for studying the ZF universe." (Paul E. Howard, Mathematical Reviews, Issue 2007 f), From the reviews: "The book is an excellent introduction to the Axiom of Choice, its consequences and even its possible replacements. Although the author claims not to have written a textbook, compendium or history, the book might be used as any of these three. … there are many diagrams throughout the text and in the appendix detailing the relationships between the Axiom of Choice and its consequences. It certainly fulfills its stated purpose of whetting the reader's appetite for studying the ZF universe." (Paul E. Howard, Mathematical Reviews, Issue 2007 f), From the reviews: "The book is an excellent introduction to the Axiom of Choice, its consequences and even its possible replacements. Although the author claims not to have written a textbook, compendium or history, the book might be used as any of these three. ... there are many diagrams throughout the text and in the appendix detailing the relationships between the Axiom of Choice and its consequences. It certainly fulfills its stated purpose of whetting the reader's appetite for studying the ZF universe." (Paul E. Howard, Mathematical Reviews, Issue 2007 f)
Dewey Edition22
Series Volume Number1876
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal511.3
Table Of ContentOrigins: Hilbert's First Problem.- Choice Principles: Some Equivalents to the Axiom of Choice, Some Concepts Related to the Axiom of Choice.- Elementary Observations: Hidden Choice, Unnecessary Choice, Concepts Split Up: Compactness.- Disasters without Choice: Finiteness, Disasters in Cardinal Arithmetic, Disasters in Order Theory, Disasters in Algebra I: Vector Spaces, Disasters in Algebra II: Categories, Disasters in Elementary Analysis: The Reals and Continuity, Disasters in Topology I: Countable Sums, Disasters in Topology II: Products (The Tychonoff and the Cech-Stone Theorem), Disasters in Topology III: Function Spaces (The Ascoli Theorem), Disasters in Topology IV: The Baire Category Theorem, Disasters in Graph Theory: Coloring Problems.- Disasters with Choice: Disasters in Elementary Analysis, Disasters in Geometry: Paradoxical Decompositions.- Disasters either way: Disasters in Game Theory.- Beauty without Choice: Lindelöf = Compact, Measurability (The Axiom of Determinateness).
SynopsisAC, 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., AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: - Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). - Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). - Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). 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.
LC Classification NumberQA8.9-10.3
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