Cantorian Set Theory and Limitation of Size

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Clarendon Press, 1986 - Mathematics - 343 pages
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Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
 

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Contents

The Cantorian origins of set theory
1
Cantors theory of infinity
12
The ordinal theory of powers
49
Cantors theory of number
119
The origin of the limitation of size idea
165
The limitation of size argument and axiomatic set theory
195
The completability of sets
214
The Zermelo system
240
Von Neumanns reinstatement of the ordinal theory of size
270
Conclusion
299
Bibliography
307
Name index
321
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Naturalism in Mathematics
Penelope Maddy
No preview available - 1997
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About the author (1986)

Michael Hallett is at McGill University, Montreal.

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