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Introduction to Axiomatic Set Theory
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Catalogue Information
Field name
Details
Dewey Class
510
Title
Introduction to Axiomatic Set Theory ([EBook] /) / by Gaisi Takeuti, Wilson M. Zaring.
Author
Takeuti, Gaisi
Added Personal Name
Zaring, Wilson M.
author.
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : : Springer New York : : Imprint: Springer, , 1971.
Physical Details
VII, 251 p. : online resource.
Series
Graduate texts in mathematics
0072-5285 ; ; 1
ISBN
9781468499155
Summary Note
In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the 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 highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.:
Contents note
1 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 Cardinal Numbers -- 11 The Axiom of Choice, the Generalized Continuum Hypothesis and Cardinal Arithmetic -- 12 Models -- 13 Absoluteness -- 14 The Fundamental Operations -- 15 The Gödel Model -- 16 The Arithmetization of Model Theory -- 17 Cohen’s Method -- 18 Forcing -- 19 Languages, Structures, and Models -- Problem List -- Index of Symbols.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4684-9915-5
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Subject References:
Mathematics
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Mathematics, general
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Authors:
Takeuti, Gaisi
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Zaring, Wilson M.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Graduate texts in mathematics
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GTM
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Classification:
510
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