# Notes on Set Theory

Springer Science & Business Media, 1994 - 272 páginas
"The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets." "Topics covered include the naive theory of equinumerosity; paradoxes and axioms; modeling mathematical notions by sets; cardinal numbers; natural numbers; fixed points (continuous least-fixed-point theorem); well-ordered sets (transfinite induction and recursion, Hartogs' theorem, comparability of well-ordered sets, least-fixed-point theorem); the Axiom of Choice and its consequences; Baire space (Cantor-Bendixson theorem, analytic pointsets, perfect set theorem); Replacement and other axioms; ordinal numbers. There is an Appendix on the real numbers and another on natural models, including the antifounded universe." "The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy."--BOOK JACKET.

### Comentarios de la gente -Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### Contenido

 Introduction 1 Equinumerosity 7 Paradoxes and axioms 19 Are sets all there is? 33 The natural numbers 53 Fixed points 73 Well ordered sets 93 Choices 117
 Baire space 147 Replacement and other axioms 169 Ordinal numbers 189 A The real numbers 209 B Axioms and universes 239 Index 267 Derechos de autor