000			a
999			_c32301 _d32301
008			231011b xxu||||| |||| 00| 0 eng d
020			_a9781107120327
082			_a511.322 _bCUN
100			_aCunningham, Daniel W.
245			_aSet theory : a first course
260			_bCambridge University Press, _c2016 _aNew York :
300			_axii, 250 p. ; _bill., _c24 cm.
365			_b45.99 _cGBP _d109.80
490			_aCambridge mathematical textbooks
504			_aIncludes bibliographical references and indexes.
520			_aSet theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
650			_aCardinal numbers
650			_a Ordinal numbers
650			_aAxiom of choice
650			_aTransfinite recursion;
650			_aAbstract sets
650			_aAxiomatic set theory
942			_2ddc _cBK