
	Where results make sense

Topic: Axiom schema of specification

Related Topics

axiom of choice

Separation axioms

Peano axioms

probability axioms

axiom of extensionality

Zermelo Fraenkel axioms

Axiom of regularity

Kuratowski closure axioms

Axiom schema of specification

axiom of infinity

axiom of empty set

Axiom of pairs

In the News (Sun 6 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Axiom schema of specification - Wikipedia, the free encyclopedia
		In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom schema of specification, or axiom schema of separation, or axiom schema of restricted comprehension, is a schema of axioms in Zermelo-Fraenkel set theory.
		The axiom schema of specification is generally considered uncontroversial as far as it goes, and it or an equivalent appears in just about any alternative axiomatisation of set theory.
		Most of the other Zermelo-Fraenkel axioms (but not the axiom of extensionality or the axiom of regularity) then became necessary to serve as an additional replacement for the axiom schema of comprehension; each of these axioms states that a certain set exists, and defines that set by giving a predicate for its members to satisfy.
	www.wikipedia.org /wiki/Axiom+of+comprehension (960 words)

	Axiom schema of replacement - Wikipedia, the free encyclopedia
		Then given a subset A of S, applying the axiom schema of replacement to F constructs the image f(A) of the subset A under the function f; it is just F(A).
		The axiom was independently discovered by Thoralf Skolem later in the same year, and it is in fact Skolem's final version of the axiom list that we use today -- but he usually gets no credit since each individual axiom was developed earlier by either Zermelo or Fraenkel.
		But in this case, the set B required for the axiom of specification is the empty set, so the axiom schema follows in general using also the axiom of empty set.
	en.wikipedia.org /wiki/Axiom_schema_of_replacement (1088 words)

	AXIOM SCHEMA OF SPECIFICATION FACTS AND INFORMATION (Site not responding. Last check: 2007-11-06)
		In axiomatic_set_theory and the branches of logic, mathematics, and computer_science that use it, the axiom schema of specification, or axiom schema of separation, or axiom schema of restricted comprehension, is a schema of axioms in Zermelo-Fraenkel_set_theory.
		This axiom schema was tacitly used in the early days of naive_set_theory, before a strict axiomatisation was adopted.
		Most of the other Zermelo-Fraenkel axioms (but not the axiom_of_extensionality or the axiom_of_regularity) then became necessary to serve as an additional replacement for the axiom schema of comprehension; each of these axioms states that a certain set exists, and defines that set by giving a predicate for its members to satisfy.
	www.southcountryequity.com /Axiom_schema_of_specification (989 words)

	Schema article - Schema Greek formal logic recursively definable infinite axiom schema - What-Means.com (Site not responding. Last check: 2007-11-06)
		The word schema comes from the Greek word "σχήμα" (schema) that means shape or more generally plan.
		For example, the axiom schema of replacement is a schema of axioms in axiomatic set theory.
		An XML schema provides a means for defining the structure, content and to some extent, the semantics of XML documents.
	www.what-means.com /encyclopedia/Schema (294 words)

	Axiom of replacement (Site not responding. Last check: 2007-11-06)
		The axiom schema of replacement wasn't part of Ernst Zermelo 's 1908 axiomatisation of set theory (Z); its introduction by Adolf Fraenkel in 1922 is what makesmodern set theory Zermelo-Fraenkel set theory (ZF).
		The axiom was independently discovered by Thoralf Skolem later in the same year, and it is in fact Skolem's final versionof the axiom list that we use today -- but he usually gets no credit since each individual axiom was developed earlier by eitherZermelo or Fraenkel.
		The axiom schema of specification canalmost be derived from the axiom schema of replacement.
	www.therfcc.org /axiom-of-replacement-160926.html (1016 words)

	SetTheory - PineWiki
		In reading the statement of the axiom, you should think of x as the set we are taking a union over, y as the union ∪x, z as some element that might or might not be in y, and q as an element of x that contains z and thus puts z in the union.
		This is an "axiom schema" instead of an axiom, because it defines an infinite family of axioms, one for each choice of P. Naive set theory adopts the simpler approach of getting rid of the parent set x, and allowing you to define a set { x
		Finally, we have one final axiom, which is generally accepted by mathematicians because it's convenient but is in a very real sense optional, in that the rest of the axioms are consistent with either it or its negation.
	pine.cs.yale.edu /pinewiki/SetTheory (4111 words)

	Axiom schema of specification (Site not responding. Last check: 2007-11-06)
		Thus what the axiom schema is saying is that given a set A and a predicate P we can find a subset B of A whose members are precisely the members A that satisfy P.
		The axiom schema of specification is generally uncontroversial as far as it goes and or an equivalent appears in just about alternative axiomatization of set theory.
		In second-order logic we can quantify over predicates and axiom schema of specification becomes a simple This is much the same trick as used in the NBG axioms of the section where the predicate was replaced by class that was then quantified over.
	www.freeglossary.com /Axiom_of_separation (1378 words)

	<Data Minds> - tribe.net (Site not responding. Last check: 2007-11-06)
		The word axiom comes from the Greek word αξιωμα (axioma), which means that which is deemed worthy or fit or that which is considered self-evident.
		This might challenge the classical notion of axiom and is at least one of the reasons why axioms are not regarded as obviously true or self-evident statements.
		Thus, this notion of axiom is perhaps the closest to the intended meaning of the word: that axioms are true, no matter what.
	lovechao.tribe.net /thread/b117884e-cfcf-414c-a8ff-fd5be7fb0705 (2295 words)

	CONK! Encyclopedia: List_of_axioms (Site not responding. Last check: 2007-11-06)
		In epistemology, the word axiom is understood differently; see axiom and self-evidence.
		Individual axioms are almost always part of a larger axiomatic system.
		These are the de facto standard axioms for contemporary mathematics
	www.conk.com /search/encyclopedia.cgi?q=List_of_axioms (74 words)

	Axiom of union (Site not responding. Last check: 2007-11-06)
		In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of union is one ofthe axioms of Zermelo-Fraenkel set theory, stating that, for any two sets, there is a set that contains theexactly elements of both.
		The axiom of union is generally considered uncontroversial, and it or an equivalent appears in just about any alternative axiomatization of set theory.
		A as {C inB : for all D in A, C is in D} using the axiom schema of specification.
	www.therfcc.org /axiom-of-union-160925.html (304 words)

	Axiom of power set - Encyclopedia Glossary Meaning Explanation Axiom of power set (Site not responding. Last check: 2007-11-06)
		Axiom of power set - Encyclopedia Glossary Meaning Explanation Axiom of power set.
		In mathematics, the axiom of power set is one of the Zermelo-Fraenkel axioms of axiomatic set theory.
		The axiom of power set is generally considered uncontroversial, and it or an equivalent appears in just about any alternative axiomatisation of set theory.
	www.encyclopedia-glossary.com /en/Axiom-of-power-set.html (229 words)

	Axiom schema of specification : Axiom schema of comprehension
		Axiom schema of specification : Axiom schema of comprehension
		The predicate (C isn't in C) is forbidden, because the same symbol C appears on both sides of the membership symbol; thus, Russell's paradox is avoided.
		All is still licensed under the GNU FDL.
	www.wordlookup.net /ax/axiom-schema-of-comprehension.html (1296 words)

	Absolute Infinite - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		This seems paradoxical, and is closely related to Cesare Burali-Forti's "paradox" that there can be no greatest ordinal number.
		There is a quick fix in Zermelo's system by his Axiom of Separation, which stipulates that sets cannot be independently defined by any arbitrary logically definable notion, but must be separated as subsets of sets already "given".
		This, he says, eliminates contradictory ideas like "the set of all sets" or "the set of all ordinal numbers".
	www.bexley.us /project/wikipedia/index.php/Absolute_infinite (577 words)

	Category:Set theory (Site not responding. Last check: 2007-11-06)
		Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's paradox) in naive set theory.
		It treats sets as "whatever satisfies the axioms", and the notion of collections of things serves only as motivation for the axioms.
		Internal set theory is an axiomatic extension of set theory that supports a logically consistent identification of illimited (enormously large) and infinitesimal elements within the real numbers.
	www.tocatch.info /en/Category:Set_theory.htm (164 words)

	mediterranean.ca - Axiom schema (Site not responding. Last check: 2007-11-06)
		We couldn't find any results for Axiom schema in Books.
		Here are some other items you may be interested in.
		Edit, Validate, Generate & Convert XML Schemas - Download a Free Trial.
	www.mediterranean.ca /Axiom-schema/reference/fullview/wikipedia/764613 (50 words)

	axiom schema - OneLook Dictionary Search (Site not responding. Last check: 2007-11-06)
		Tip: Click on the first link on a line below to go directly to a page where "axiom schema" is defined.
		Axiom Schema : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include axiom schema: axiom schema of separation, axiom schema of comprehension, axiom schema of replacement, axiom schema of specification
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=axiom+schema (93 words)

	Axiom schema of specification : Axiom schema of separation (Site not responding. Last check: 2007-11-06)
		Axiom schema of specification : Axiom schema of separation
		Axiom schema of specification : Axiom schema of separation
		It uses material from the wikipedia article Axiom schema of specification : Axiom schema of separation.
	www.eurofreehost.com /ax/Axiom_schema_of_separation.html (397 words)

	laughing.ca - Axiom of empty set (Site not responding. Last check: 2007-11-06)
		We couldn't find any results for Axiom of empty set in DVD.
		Top industry pros are conducting a nationwide search for comedians to do their bit live and see if they are ready to take the next step in their careers with a shot at the big time.
		This is YOUR forum to speak out on the Hurricane Katrina disaster.
	www.laughing.ca /Axiom-of-empty-set/web/search (204 words)

	axiom schema of specification - OneLook Dictionary Search (Site not responding. Last check: 2007-11-06)
		axiom schema of specification - OneLook Dictionary Search
		We found one dictionary with English definitions that includes the word axiom schema of specification:
		Tip: Click on the first link on a line below to go directly to a page where "axiom schema of specification" is defined.
	www.onelook.com /?w=axiom+schema+of+specification (85 words)

	Fatbomb/Baby Sitter (Site not responding. Last check: 2007-11-06)
		A comprehensive directory of public dump stations across the United States.
		power set -- Axiom of regularity -- Axiom schema of replacement -- Axiom schema of specification -- Axiomatic set theory -- Axiomatic system -- Axiomatization -- B B-spline -- B-star-algebra -- Babbage -- Babbage, Charles -- Babington plot -- Baby Monster group -- Babylonian numerals -- Backward inorder traversal -- Baez, John -- Bailey,
		Miscellaneous A BABY-SITTER who murdered a boy of two by beating his head against a stair banister last night faced life in jail.Mum-of-two Susan Holdsworth, 34, who was looking...
	bonose.com /Fatbomb/Baby+Sitter.html (452 words)

Try your search on: Qwika (all wikis)