Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Hereditarily_countable_set> ?p ?o. }
Showing items 1 to 32 of
32
with 100 items per page.
- Hereditarily_countable_set abstract "In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. This inductive definition is in fact well-founded and can be expressed in the language of first-order set theory. A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable. If the axiom of countable choice holds, then a set is hereditarily countable if and only if its transitive closure is countable. The class of all hereditarily countable sets can be proven to be a set from the axioms of Zermelo–Fraenkel set theory (ZF) without any form of the axiom of choice, and this set is designated . The hereditarily countable sets form a model of Kripke–Platek set theory with the axiom of infinity (KPI), if the axiom of countable choice is assumed in the metatheory.If , then .More generally, a set is hereditarily of cardinality less than κ if and only it is of cardinality less than κ, and all its elements are hereditarily of cardinality less than κ; the class of all such sets can also be proven to be a set from the axioms of ZF, and is designated . If the axiom of choice holds and the cardinal κ is regular, then a set is hereditarily of cardinality less than κ if and only if its transitive closure is of cardinality less than κ.".
- Hereditarily_countable_set wikiPageExternalLink 2273380.
- Hereditarily_countable_set wikiPageID "5126046".
- Hereditarily_countable_set wikiPageRevisionID "544378548".
- Hereditarily_countable_set hasPhotoCollection Hereditarily_countable_set.
- Hereditarily_countable_set subject Category:Large_cardinals.
- Hereditarily_countable_set subject Category:Set_theory.
- Hereditarily_countable_set type Bishop109857200.
- Hereditarily_countable_set type Cardinal109894143.
- Hereditarily_countable_set type CausalAgent100007347.
- Hereditarily_countable_set type Clergyman109927451.
- Hereditarily_countable_set type LargeCardinals.
- Hereditarily_countable_set type Leader109623038.
- Hereditarily_countable_set type LivingThing100004258.
- Hereditarily_countable_set type Object100002684.
- Hereditarily_countable_set type Organism100004475.
- Hereditarily_countable_set type Person100007846.
- Hereditarily_countable_set type PhysicalEntity100001930.
- Hereditarily_countable_set type Priest110470779.
- Hereditarily_countable_set type SpiritualLeader109505153.
- Hereditarily_countable_set type Whole100003553.
- Hereditarily_countable_set type YagoLegalActor.
- Hereditarily_countable_set type YagoLegalActorGeo.
- Hereditarily_countable_set comment "In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. This inductive definition is in fact well-founded and can be expressed in the language of first-order set theory. A set is hereditarily countable if and only if it is countable, and every element of its transitive closure is countable. If the axiom of countable choice holds, then a set is hereditarily countable if and only if its transitive closure is countable.".
- Hereditarily_countable_set label "Hereditarily countable set".
- Hereditarily_countable_set label "继承可数集合".
- Hereditarily_countable_set sameAs m.0d3yv8.
- Hereditarily_countable_set sameAs Q5737810.
- Hereditarily_countable_set sameAs Q5737810.
- Hereditarily_countable_set sameAs Hereditarily_countable_set.
- Hereditarily_countable_set wasDerivedFrom Hereditarily_countable_set?oldid=544378548.
- Hereditarily_countable_set isPrimaryTopicOf Hereditarily_countable_set.