Set Theory and the Continuum Hypothesis
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic.
In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt Gödel's proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.
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assume Axiom of Choice Axiom of Infinity Axiom of Regularity Axiom of Replacement axioms of ZF cardinality clearly complete sequence consider Consis ZF consistent constant symbols contain Continuum Hypothesis contradiction COROLLARY corresponding countable ordinals defined denote elements enumerate equations existence finite sets follows forcing conditions formal system free variable G6del's give given Godel hence implies Incompleteness Theorem infinite initial segment integers introduce intuitively isomorphic LEMA LEMMA limited statement mathematics ment model for ZF notion one-one p.r. function Pn forces Power Set Axiom precisely problem proof provable prove Q forces quantifiers range of f real numbers recursive functions relation symbols relativized Replacement Axiom result rules set of integers set theory standard model subset tion transfinite induction transitive set true uncountable unique valid statement weakly forces well-founded well-ordered sets y e x