Set Theory An Introduction To Independence Proofs: 102 (Studies in Logic and the Foundations of Mathematics): Volume 102 - Hardcover

Kenneth Kunen

Hardcover

ISBN 10: 0444868399 ISBN 13: 9780444868398

Publisher: North Holland, 1983

Synopsis

Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

About this title

Synopsis

Many branches of abstract mathematics have been affected by the modern independence proofs in set theory. This book provides an introduction to relative consistency proofs in axiomatic set theory, and is intended to be used as a text in beginning graduate courses in that subject. It is hoped that this treatment will make the subject accessible to those mathematicians whose research is sensitive to axiomatics. The readers should have had the equivalent of an undergraduate course on cardinals and ordinals, but no specific training in logic is necessary. The volume includes a discussion of modern techniques in forcing, as well as coverage of infinitary combinatorics and its relevance to independence proofs. The work also features a lucid treatment of basic facts about constructibility.

Edition details

• Publisher: North Holland
• Publication date: 1983
• Language: English
• ISBN 10: 0444868399
• ISBN 13: 9780444868398
• Binding: Hardcover
• Number of pages: 330