KENNETH KUNEN SET THEORY PDF

Herbert Kenneth Kunen born August 2, is an emeritus professor of mathematics at the University of Wisconsin—Madison [1] who works in set theory and its applications to various areas of mathematics, such as set-theoretic topology and measure theory. He also works on non-associative algebraic systems, such as loops , and uses computer software, such as the Otter theorem prover , to derive theorems in these areas. Away from the area of large cardinals, Kunen is known for intricate forcing and combinatorial constructions. He proved that it is consistent that Martin's axiom first fails at a singular cardinal and constructed under the continuum hypothesis a compact L-space supporting a nonseparable measure.

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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. 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. Mathematical logic and foundations.

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