Weaver explains the basic machinery of forcing to fellow mathematics assuming no background in logic beyond the facility with formal syntax that should be second nature to any well trained mathematician. He emphasizes applications outside of set theory that were previously only available in the primary literature. His topics include Zermelo-Fraenkel set theory, ordinals and cardinals, reflection generic extensions, the fundamental theorem, families of entire functions, the diamond principle, Suslin's problem, a stronger diamond, Whitehead's problem, iterated forcing, the open coloring axiom, automorphisms of the Calkin algebra, and the multiverse interpretation. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have renewed interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
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