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The Resource Axiom of Choice, by Horst Herrlich, (electronic resource)
Axiom of Choice, by Horst Herrlich, (electronic resource)
Resource Information
The item Axiom of Choice, by Horst Herrlich, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Axiom of Choice, by Horst Herrlich, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 AC, the axiom of choice, because of its nonconstructive 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
 Language
 eng
 Extent
 XIV, 194 p. Also available online.
 Contents

 Origins: 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 CechStone 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: LindelĂ¶f = Compact, Measurability (The Axiom of Determinateness)
 Isbn
 9783540342687
 Label
 Axiom of Choice
 Title
 Axiom of Choice
 Statement of responsibility
 by Horst Herrlich
 Subject

 Algebra
 Topology
 Logic, Symbolic and mathematical
 Combinatorics
 General Algebraic Systems
 Functional analysis
 Game Theory, Economics, Social and Behav. Sciences
 Mathematical Logic and Foundations
 Functional Analysis
 Topology
 Logic, Symbolic and mathematical
 Combinatorics
 Electronic resources
 Functional Analysis
 Mathematics
 Mathematics
 Algebra
 Functional analysis
 Language
 eng
 Summary
 AC, the axiom of choice, because of its nonconstructive 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
 http://library.link/vocab/creatorName
 Herrlich, Horst
 Image bit depth
 0
 LC call number
 QA8.910.3
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Lecture Notes in Mathematics,
 Series volume
 1876
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Functional analysis
 Combinatorics
 Logic, Symbolic and mathematical
 Topology
 Mathematics
 Mathematical Logic and Foundations
 General Algebraic Systems
 Functional Analysis
 Game Theory, Economics, Social and Behav. Sciences
 Combinatorics
 Topology
 Label
 Axiom of Choice, by Horst Herrlich, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Origins: 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 CechStone 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: LindelĂ¶f = Compact, Measurability (The Axiom of Determinateness)
 Dimensions
 unknown
 Extent
 XIV, 194 p. Also available online.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783540342687
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/11601562
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783540342687
 Label
 Axiom of Choice, by Horst Herrlich, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Origins: 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 CechStone 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: LindelĂ¶f = Compact, Measurability (The Axiom of Determinateness)
 Dimensions
 unknown
 Extent
 XIV, 194 p. Also available online.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783540342687
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/11601562
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783540342687
Subject
 Algebra
 Algebra
 Combinatorics
 Combinatorics
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Game Theory, Economics, Social and Behav. Sciences
 General Algebraic Systems
 Logic, Symbolic and mathematical
 Logic, Symbolic and mathematical
 Mathematical Logic and Foundations
 Mathematics
 Mathematics
 Topology
 Topology
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