Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Axiom_schema_of_replacement> ?p ?o }
- Axiom_schema_of_replacement abstract "In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZFC.The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas.".
- Axiom_schema_of_replacement thumbnail Axiom_schema_of_replacement.svg?width=300.
- Axiom_schema_of_replacement wikiPageID "52387".
- Axiom_schema_of_replacement wikiPageLength "16913".
- Axiom_schema_of_replacement wikiPageOutDegree "70".
- Axiom_schema_of_replacement wikiPageRevisionID "682080128".
- Axiom_schema_of_replacement wikiPageWikiLink Abraham_Fraenkel.
- Axiom_schema_of_replacement wikiPageWikiLink Adolf_Fraenkel.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_choice.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_empty_set.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_foundation.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_infinity.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_limitation_of_size.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_power_set.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_regularity.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_of_separation.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_schema_of_separation.
- Axiom_schema_of_replacement wikiPageWikiLink Axiom_schema_of_specification.
- Axiom_schema_of_replacement wikiPageWikiLink Binary_relation.
- Axiom_schema_of_replacement wikiPageWikiLink Borel_determinacy_theorem.
- Axiom_schema_of_replacement wikiPageWikiLink Borel_set.
- Axiom_schema_of_replacement wikiPageWikiLink Cardinal_number.
- Axiom_schema_of_replacement wikiPageWikiLink Cardinality.
- Axiom_schema_of_replacement wikiPageWikiLink Category:Axioms_of_set_theory.
- Axiom_schema_of_replacement wikiPageWikiLink Class_(set_theory).
- Axiom_schema_of_replacement wikiPageWikiLink Congress_of_Scandinavian_Mathematicians.
- Axiom_schema_of_replacement wikiPageWikiLink Consistency.
- Axiom_schema_of_replacement wikiPageWikiLink Constructive_set_theory.
- Axiom_schema_of_replacement wikiPageWikiLink Countable.
- Axiom_schema_of_replacement wikiPageWikiLink Countable_set.
- Axiom_schema_of_replacement wikiPageWikiLink Determinacy.
- Axiom_schema_of_replacement wikiPageWikiLink Disjoint_union.
- Axiom_schema_of_replacement wikiPageWikiLink Dmitry_Mirimanoff.
- Axiom_schema_of_replacement wikiPageWikiLink Ernst_Zermelo.
- Axiom_schema_of_replacement wikiPageWikiLink First_uncountable_ordinal.
- Axiom_schema_of_replacement wikiPageWikiLink Functional_predicate.
- Axiom_schema_of_replacement wikiPageWikiLink German_Mathematical_Society.
- Axiom_schema_of_replacement wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Axiom_schema_of_replacement wikiPageWikiLink Gxc3xb6dels_second_incompleteness_theorem.
- Axiom_schema_of_replacement wikiPageWikiLink Hartogs_number.
- Axiom_schema_of_replacement wikiPageWikiLink Heinz-Dieter_Ebbinghaus.
- Axiom_schema_of_replacement wikiPageWikiLink Helsinki.
- Axiom_schema_of_replacement wikiPageWikiLink If_and_only_if.
- Axiom_schema_of_replacement wikiPageWikiLink Image_(mathematics).
- Axiom_schema_of_replacement wikiPageWikiLink Jena.
- Axiom_schema_of_replacement wikiPageWikiLink John_von_Neumann.
- Axiom_schema_of_replacement wikiPageWikiLink Large_cardinal.
- Axiom_schema_of_replacement wikiPageWikiLink Law_of_excluded_middle.
- Axiom_schema_of_replacement wikiPageWikiLink Limit_ordinal.
- Axiom_schema_of_replacement wikiPageWikiLink Logical_form.
- Axiom_schema_of_replacement wikiPageWikiLink Mirimanoff.
- Axiom_schema_of_replacement wikiPageWikiLink Model_(logic).
- Axiom_schema_of_replacement wikiPageWikiLink Ordinal_number.
- Axiom_schema_of_replacement wikiPageWikiLink Paul_Halmos.
- Axiom_schema_of_replacement wikiPageWikiLink Power_set.
- Axiom_schema_of_replacement wikiPageWikiLink Proof-theoretic.
- Axiom_schema_of_replacement wikiPageWikiLink Proof_theory.
- Axiom_schema_of_replacement wikiPageWikiLink Proper_class.
- Axiom_schema_of_replacement wikiPageWikiLink Rank_(set_theory).
- Axiom_schema_of_replacement wikiPageWikiLink Relation_(mathematics).
- Axiom_schema_of_replacement wikiPageWikiLink Schema_(logic).
- Axiom_schema_of_replacement wikiPageWikiLink Second-order_arithmetic.
- Axiom_schema_of_replacement wikiPageWikiLink Set-builder_notation.
- Axiom_schema_of_replacement wikiPageWikiLink Set_(mathematics).
- Axiom_schema_of_replacement wikiPageWikiLink Set_theory.
- Axiom_schema_of_replacement wikiPageWikiLink Skolems_paradox.
- Axiom_schema_of_replacement wikiPageWikiLink Structure_(mathematical_logic).
- Axiom_schema_of_replacement wikiPageWikiLink Subset.
- Axiom_schema_of_replacement wikiPageWikiLink Superset.
- Axiom_schema_of_replacement wikiPageWikiLink Surjection.
- Axiom_schema_of_replacement wikiPageWikiLink Surjective_function.
- Axiom_schema_of_replacement wikiPageWikiLink Thoralf_Skolem.
- Axiom_schema_of_replacement wikiPageWikiLink Topos.
- Axiom_schema_of_replacement wikiPageWikiLink Type_theory.
- Axiom_schema_of_replacement wikiPageWikiLink Von_Neumann.
- Axiom_schema_of_replacement wikiPageWikiLink Von_Neumann_cardinal_assignment.
- Axiom_schema_of_replacement wikiPageWikiLink Von_Neumann_ordinal.
- Axiom_schema_of_replacement wikiPageWikiLink Von_Neumann_universe.
- Axiom_schema_of_replacement wikiPageWikiLink Well-order.
- Axiom_schema_of_replacement wikiPageWikiLink Well-ordered_set.
- Axiom_schema_of_replacement wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Axiom_schema_of_replacement wikiPageWikiLink File:Axiom_schema_of_replacement.svg.
- Axiom_schema_of_replacement wikiPageWikiLink File:Codomain2_A_B.SVG.
- Axiom_schema_of_replacement wikiPageWikiLinkText "Axiom schema of replacement".
- Axiom_schema_of_replacement wikiPageWikiLinkText "Axiom_schema_of_replacement".
- Axiom_schema_of_replacement wikiPageWikiLinkText "Collection".
- Axiom_schema_of_replacement wikiPageWikiLinkText "Replacement".
- Axiom_schema_of_replacement wikiPageWikiLinkText "axiom of replacement".
- Axiom_schema_of_replacement wikiPageWikiLinkText "axiom schema of collection".
- Axiom_schema_of_replacement wikiPageWikiLinkText "axiom schema of replacement".
- Axiom_schema_of_replacement wikiPageWikiLinkText "collection".
- Axiom_schema_of_replacement wikiPageWikiLinkText "help of Skolem".
- Axiom_schema_of_replacement wikiPageWikiLinkText "replacement axiom".
- Axiom_schema_of_replacement wikiPageWikiLinkText "replacement".
- Axiom_schema_of_replacement hasPhotoCollection Axiom_schema_of_replacement.
- Axiom_schema_of_replacement wikiPageUsesTemplate Template:More_footnotes.
- Axiom_schema_of_replacement wikiPageUsesTemplate Template:Reflist.
- Axiom_schema_of_replacement wikiPageUsesTemplate Template:Set_theory.
- Axiom_schema_of_replacement subject Category:Axioms_of_set_theory.