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Set Theory and its PhilosophyA Critical Introduction$
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Michael Potter

Print publication date: 2004

Print ISBN-13: 9780199269730

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199269730.001.0001

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Ordinal arithmetic

Ordinal arithmetic

Chapter:
(p.191) Chapter 12 Ordinal arithmetic
Source:
Set Theory and its Philosophy
Author(s):

Michael Potter (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199269730.003.0017

This chapter defines operations of addition, multiplication, and exponentiation for ordinals. It takes as a model the recursive definitions of the corresponding operations for natural numbers (§ 5.4): the form the extended definitions should take at success or ordinals is clear; the form of the additional clause defining the behaviour of the operations at limit ordinals is also clear if it is required that the operations must all be normal in their second variable.

Keywords:   ordinals, additionan, multiplication, exponentiation, natural numbers

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