Axiom of Choice

Axiom of Choice by Horst Herrlich.

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...

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Bibliographic Details
Main Author: Herrlich, Horst (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2006.
Edition:1st ed. 2006.
Series:Lecture Notes in Mathematics, 1876
Springer eBook Collection.
Subjects:
Mathematical logic.
Algebra.
Functional analysis.
Game theory.
Combinatorics.
Topology.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of 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 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).

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