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

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, Martins axiom, almost disjoint and quasidisjoint sets, trees, extensionality and comprehension, relations, functions, and wellordering, ordinals, cardinals, and real numbers. The manuscript then ponders on wellfounded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of wellfounded sets, and induction and recursion on wellfounded 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.