  View Basket     AiML Academia Brasileira de Filosofia Algorithmics Cadernos de Lógica e Computação Cadernos de Lógica e Filosofia Cahiers de Logique et d'Epistemologie Communication, Mind and Language Computing Cuadernos de lógica, Epistemología y Lenguaje DEON Dialogues Economics Encyclopaedia of Logic Filosofia Handbooks Historia Logicae IfColog series in Computational Logic Journal of Applied Logics - IfCoLog Journal Journals Landscapes Logics for New-Generation AI Logic and Law Logic and Semiotics Logic PhDs Logic, Methodology and Philosophy of Science The Logica Yearbook Neural Computing and Artificial Intelligence Philosophy Research The SILFS series Studies in Logic History of Logic Logic and cognitive systems Mathematical logic and foundations Studies in Logic and Argumentation Studies Student Publications Systems Texts in Logic and Reasoning Texts in Mathematics Tributes Other Digital Downloads Information for authors About us Search for Books  Mathematical logic and foundations Back Set TheoryKenneth KunenThis book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models in which CH is false. More generally, cardinal exponentiation on the regular cardinals can consistently be anything not contradicting the classical theorems of Cantor and König. The basic methods for the independence proofs are the notion of constructibility, introduced by Gödel, and the method of forcing, introduced by Cohen. This book describes these methods in detail, verifi es the basic independence results for cardinal exponentiation, and also applies these methods to prove the independence of various mathematical questions in measure theory and general topology. Before the chapters on forcing, there is a fairly long chapter on “infi nitary combinatorics”. This consists of just mathematical theorems (not independence results), but it stresses the areas of mathematics where set-theoretic topics (such as cardinal arithmetic) are relevant. There is, in fact, an interplay between infi nitary combinatorics and independence proofs. Infi nitary combinatorics suggests many set-theoretic questions that turn out to be independent of ZFC, but it also provides the basic tools used in forcing arguments. In particular, Martin’s Axiom, which is one of the topics under infi nitary combinatorics, introduces many of the basic ingredients of forcing.2 November 2011978-1-84890-050-9

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