Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics (Science Networks Historical Studies, Vol. 23)

Rok: 1999
ISBN: 9783764357498
OKCZID: 110103133

Hodnocení: 5.0 / 5 (6 hlasů)

Anotace

This new book discusses the emergence and development of the notion of set theory during the period 1850-1950. Instead of focusing directly on the development of set theory, in the technical sense of the expression, and therefore on the figure of Georg Cantor, it addresses a wider issue: Why did German mathematicians pay attention to the notion of sets? What were their motivations? How did set theory turn into a branch of mathematics? How did our present conception of it become widely accepted? The focus is more on the development of research programs, than on technical result attained. Therefore the work will be of interest not only to mathematicians, but to philosophers and historians of science too. The book is divided in three parts. The first, devoted to the emergence of sets from within several branches of mathematics (function theory, geometry, algebra, algebraic number theory, real analysis), incorporates the novelty of discussing the role played by Bernhard Riemann in the earliest phases of the story. The second deals with the early set theories, including a compact study of Cantor's research program and his path-breaking contributions, together with an analysis of the parallel work of Dedekind, and a discussion of the complex interactions between the two mathematicians. The third part studies the period from the paradoxes to Gdel's independence results, during which set theory was finally incorporated into mainstream mathematics. Attention is also devoted to type theory, then a powerful alternative to set theory, although the period ended with the triumph of modern first-order set theory. Series: Science Networks. Historical Studies, Vol. 23

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