von neumann ordinal

Computing Dictionary

von Neumann ordinal definition

mathematics
An implementation of ordinals in set theory (e.g. Zermelo Fränkel set theory or ZFC). The von Neumann ordinal alpha is the well-ordered set containing just the ordinals "shorter" than alpha.
"Reasonable" set theories (like ZF) include Mostowski's Collapsing Theorem: any well-ordered set is isomorphic to a von Neumann ordinal. In really screwy theories (e.g. NFU -- New Foundations with Urelemente) this theorem is false.
The finite von Neumann ordinals are the von Neumann integers.
(1995-03-30)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
Cite This Source
Explore Dictionary.com
Previous Definition: von neumann machine
Next Definition: von neumann, john
More from Thesaurus.com
Synonyms and Antonyms for von neumann ordinal
More from Reference.com
Search for articles containing von neumann ordinal
Dictionary.com Word FAQs

Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.

Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature