The Theory of Sets and Transfinite Arithmetic [Book Review]

Review of Metaphysics 19 (3):578-579 (1966)
  Copy   BIBTEX

Abstract

This is a text for a one or two semester course on axiomatic set theory; the goal is to introduce and develop one system of set theory in a complete and thorough way, presupposing only the elusive "mathematical maturity" of the reader. There are nine chapters which begin with a development of propositional and predicate logic oriented toward set theory and develop the Zermelo-Fraenkel system in exceptional detail. The book starts slowly, the first 120 pages being devoted to logical preliminaries and the introduction of axioms; it gathers speed, however, and the remaining chapters include treatment of the algebra of classes, relations and functions, order of various sorts and Zorn's lemma, real numbers and equivalence classes, the equipollence of sets, similarity as a relation of sets, the ordinal numbers and their arithmetic, the cardinal numbers and their arithmetic. These later chapters are extremely detailed and comprehensive, presenting a wealth of material. There are numerous exercises, many quite difficult, at the end of each chapter, along with a summary of that chapter's content. Because of the single-mindedness of the book, there is little reference to other systems of set theory, but this is not a drawback at all. The presentation is orthodox, but not dull; careful, but not generally pedantic or repetitive. This makes it a good text for self-study.—P. J. M.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,656

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2012-03-18

Downloads
23 (#584,666)

6 months
1 (#1,042,085)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references