The Joy of Sets: Fundamentals of Contemporary Set TheorySpringer Science & Business Media, 6 dec 2012 - 194 pagina's This book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics. The intended reader is either an advanced-level mathematics undergraduate, a beginning graduate student in mathematics, or an accomplished mathematician who desires or needs some familiarity with modern set theory. The book is written in a fairly easy-going style, with minimal formalism. In Chapter 1, the basic principles of set theory are developed in a 'naive' manner. Here the notions of 'set', 'union', 'intersection', 'power set', 'rela tion', 'function', etc., are defined and discussed. One assumption in writing Chapter 1 has been that, whereas the reader may have met all of these 1 concepts before and be familiar with their usage, she may not have con sidered the various notions as forming part of the continuous development of a pure subject (namely, set theory). Consequently, the presentation is at the same time rigorous and fast. |
Inhoudsopgave
1 | |
The ZermeloFraenkel Axioms | 41 |
Ordinal and Cardinal Numbers | 66 |
Topics in Pure Set Theory | 101 |
The Axiom of Constructibility | 125 |
NonWellFounded Set Theory | 143 |
185 | |
Overige edities - Alles bekijken
The Joy of Sets: Fundamentals of Contemporary Set Theory Keith Devlin Geen voorbeeld beschikbaar - 2012 |
The Joy of Sets: Fundamentals of Contemporary Set Theory Keith Devlin Geen voorbeeld beschikbaar - 1993 |
Veelvoorkomende woorden en zinsdelen
a₁ abbreviates assume Axiom of Choice Axiom of Constructibility Axiom of Foundation Axiom of Infinity Axiom of Replacement Axiom of Subset axioms of set basic bijection binary relation bisimulation boolean algebra Clearly cofinal concept consistent constructible set theory Corollary countable defined denote easily seen elements equivalence Exercise existence extensional fact finite sets fixed-point formula of LAST Fraenkel function graph Hence inaccessible cardinal induction infinite cardinal isomorphic Let F limit ordinal logic mathematical maximal non-well-founded sets notation notion operation ordered pair poset power set proper class prove recursion principle result sequence Set Axiom set-theoretic Solution Lemma Subset Selection successor ordinal Suppose system of equations tagged Theorem theory of sets top node uncountable unique decoration VA[X w₁ well-founded well-ordering woset Zermelo hierarchy Zermelo-Fraenkel set theory ZFC axioms ZFCA