Notre Dame Mathematical Lectures

Abstract Set Theory

Thoralf A. Skolem

Book information

Author
Thoralf A. Skolem

Publication information
Notre Dame Mathematical Lectures, Number 8
1st
Notre Dame, Indiana : University of Notre Dame, 1962
70 pp.

Dates
Publication date: 1962
First available in Project Euclid: 29 March 2007

Permanent link to this book
https://projecteuclid.org/euclid.ndml/1175197470

Mathematical Reviews (MathSciNet):
MR0156776

Subjects
Set theory

Rights
Copyright © 1962, University of Notre Dame

Citation
Thoralf A. Skolem, Abstract Set Theory (Notre Dame, Ind.: University of Notre Dame, 1962)

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Title and Copyright Pagesi - ii
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Prefaceiii
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Table of Contentsv
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Chapter 1: Historical remarks; Outlines of Cantor's theory1 - 6
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Chapter II: Ordered sets; A theorem of Hausdorff7 - 11
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Chapter III: Axiomatic set theory; Axioms of Zermelo and Fraenkel12 - 19
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Chapter IV: The well-ordering theorem19 - 22
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Chapter V: Ordinals and alephs22 - 28
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Chapter VI: Some remarks on functions of ordinal numbers28 - 32
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Chapter VII: On the exponentiation of alephs32 - 34
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Chapter VIII: Set representing ordinals35 - 37
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Chapter IX: The notions "finite" and "infinite"38 - 41
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Chapter X: The simple infinite sequence; Development of arithmetic41 - 44
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Chapter XI: Some remarks on the nature of the set-theoretic axioms; The set-theoretic relativism45 - 47
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Chapter XII: The simple theory of types48 - 50
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Chapter XIII: The theory of Quine50 - 52
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Chapter XIV: The ramified theory of types. Predicative set theory52 - 61
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Chapter XV: Lorenzen's operative mathematics61 - 64
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Chapter XVI: Some remarks on intuitionist mathematics64 - 68
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Chapter XVII: Mathematics without quantifiers68 - 69
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Chapter XVIII: The possibility of set theory based on many-valued logic69 - 70
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