Classic set theory : for guided independent study / Derek Goldrei.

INTRODUCTION Outline of the book Assumed knowledge THE REAL NUMBERS Introduction Dedekind's construction Alternative constructions The rational numbers THE NATURAL NUMBERS Introduction The construction of the natural numbers Arithmetic Finite sets THE ZERMELO-FRAENKEL AXIOMS Introduction A formal language Axioms 1 to 3 Axioms 4 to 6 Axioms 7 to 9 CARDINAL (Without the Axiom of Choice) Introduction Comparing Sizes Basic properties of " and = Infinite sets without AC-countable sets Uncountable sets and cardinal arithmetic without AC ORDERED SETS Introduction Linearly ordered sets Order arithmetic Well-ordered sets ordinal numbers -- Introduction Ordinal numbers Beginning ordinal arithmetic -- Ordinal arithmetic -- The as set theory with the axiom of choice -- Introduction -- The well-ordering principle -- Cardinal arithmetic and the axiom of choice -- The continuum hypothesis

Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory