Added to Favorites

Computing Dictionary

A set theory with the following set of axioms:

Extensionality: two sets are equal if and only if they have the same elements.

Union: If U is a set, so is the union of all its elements.

Pair-set: If a and b are sets, so is

a, b.

Foundation: Every set contains a set disjoint from itself.

Comprehension (or Restriction): If P is a formula with one free variable and X a set then

x: x is in X and P(x).

is a set.

Infinity: There exists an infinite set.

Power-set: If X is a set, so is its power set.

Zermelo set theory avoids Russell's paradox by excluding sets of elements with arbitrary properties - the Comprehension axiom only allows a property to be used to select elements of an existing set.

Zermelo Fränkel set theory adds the Replacement axiom.

[Other axioms?]

(1995-03-30)

Explore Dictionary.com

Previous Definition: zermelo fränkel set theory

Next Definition: zermelo's axiom

Words Near: zermelo set theory

More from Thesaurus.com

Synonyms and Antonyms for zermelo set theory

More from Reference.com

Search for articles containing zermelo set theory

More from Dictionary.com Translator

Translate zermelo set theory into French

Translate zermelo set theory into German

Translate zermelo set theory into Italian

Translate zermelo set theory into another language

Dictionary.com Word FAQs

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

Nearby Words

Copyright © 2014 Dictionary.com, LLC. All rights reserved.