02527nmm a2200301 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245010200158250001900260260004800279300003000327505058700357653003700944653003900981653001601020700003201036710003401068041001901102989003801121490003401159856007401193082001001267520094801277EB000622792EBX0100000000000000047587400000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814613816861 aTakeuti, Gaisi00aIntroduction to Axiomatic Set TheoryhElektronische Ressourcecby Gaisi Takeuti, Wilson M. Zaring aSecond Edition aNew York, NYbSpringer New Yorkc1982, 1982 aX, 246 pbonline resource0 a1 Introduction -- 2 Language and Logic -- 3 Equality -- 4 Classes -- 5 The Elementary Properties of Classes -- 6 Functions and Relations -- 7 Ordinal Numbers -- 8 Ordinal Arithmetic -- 9 Relational Closure and the Rank Function -- 10 The Axiom of Choice and Cardinal Numbers -- 11 Cofinality, the Generalized Continuum Hypothesis, and Cardinal Arithmetic -- 12 Models -- 13 Absoluteness -- 14 The Fundamental Operations -- 15 The Gödel Model -- 16 Silver Machines -- 17 Applications of Silver Machines -- 18 Introduction to Forcing -- 19 Forcing -- Problem List -- Index of Symbols aLogic, Symbolic and mathematical aMathematical Logic and Foundations aMathematics1 aZaring, Wilson M.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aGraduate Texts in Mathematics uhttp://dx.doi.org/10.1007/978-1-4613-8168-6?nosfx=yxVerlag3Volltext0 a511.3 aIn 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text