College Publications logo   College Publications title  
View Basket
Homepage Contact page
Academia Brasileira de Filosofia
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Comptes Rendus de l'Academie Internationale de Philosophie des Sciences
Cuadernos de lógica, Epistemología y Lenguaje
Encyclopaedia of Logic
Historia Logicae
IfColog series in Computational Logic
Journal of Applied Logics - IfCoLog Journal
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
The SILFS series
Studies in Logic
History of Logic
Logic and cognitive systems
Mathematical logic and foundations
Studies in Logic and Argumentation
Logic and Bounded Rationality
Studies in Talmudic Logic
Student Publications
Texts in Logic and Reasoning
Texts in Mathematics
Digital Downloads
Information for authors
About us
Search for Books

Mathematical logic and foundations


Set Theory

Kenneth Kunen

This 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 2011


© 2005–2024 College Publications / VFH webmaster