Labyrinth of Thought discusses the emergence and development of set
theory and the set-theoretic approach to mathematics during the period
1850-1940. Rather than focusing on the pivotal figure of Georg Cantor,
it analyzes his work and the emergence of transfinite set theory
within the broader context of the rise of modern mathematics. The text
has a tripartite structure. Part 1, The Emergence of Sets within
Mathematics, surveys the initial motivations for a mathematical notion
of a set within several branches of the discipline (geometry, algebra,
algebraic number theory, real and complex analysis), emphasizing the
role played by Riemann in fostering acceptance of the set-theoretic
approach. In Part 2, Entering the Labyrinth, attention turns to the
earliest theories of sets, their evolution, and their reception by the
mathematical community; prominent are the epoch-making contributions
of Cantor and Dedekind, and the complex interactions between them.
Part 3, In Search of an Axiom System, studies the four-decade period
from the discovery of set-theoretic paradoxes to Gödel’s
independence results, an era during which set theory gradually became
assimilated into mainstream mathematics; particular attention is given
to the interactions between axiomatic set theory and modern systems of
formal logic, especially the interplay between set theory and type
theory. A new Epilogue for this second edition offers further
reflections on the foundations of set theory, including the "dichotomy
conception" and the well-known iterative conception.
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A History of Set Theory and Its Role in Modern Mathematics
Produktdetaljer
ISBN
9783764383503
Publisert
2020
Utgave
2. utgave
Utgiver
Vendor
Birkhauser
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter