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- Scotts_trick abstract "In set theory, Scott's trick is a method for giving a definition of equivalence classes for equivalence relations on a proper class (Jech 2003:65). The method relies on the axiom of regularity but not on the axiom of choice. It can be used to define representatives for ordinal numbers in ZF, Zermelo–Fraenkel set theory without the axiom of choice (Forster 2003:182). The method was introduced by Dana Scott (1955).Beyond the problem of defining set representatives for ordinal numbers, Scott's trick can be used to obtain representatives for cardinal numbers and more generally for isomorphism types, for example, order types of linearly ordered sets (Jech 2003:65). It is credited to be indispensable (even in the presence of the axiom of choice) when taking ultrapowers of proper classes in model theory. (Kanamori 1994:47)".
- Scotts_trick wikiPageID "22077085".
- Scotts_trick wikiPageLength "3667".
- Scotts_trick wikiPageOutDegree "20".
- Scotts_trick wikiPageRevisionID "676383546".
- Scotts_trick wikiPageWikiLink Aleph_number.
- Scotts_trick wikiPageWikiLink Axiom_of_choice.
- Scotts_trick wikiPageWikiLink Axiom_of_regularity.
- Scotts_trick wikiPageWikiLink Bijection.
- Scotts_trick wikiPageWikiLink Cardinal_number.
- Scotts_trick wikiPageWikiLink Cardinal_numbers.
- Scotts_trick wikiPageWikiLink Category:Set_theory.
- Scotts_trick wikiPageWikiLink Class_(set_theory).
- Scotts_trick wikiPageWikiLink Cumulative_hierarchy.
- Scotts_trick wikiPageWikiLink Equivalence_class.
- Scotts_trick wikiPageWikiLink Isomorphism_class.
- Scotts_trick wikiPageWikiLink Linear_order.
- Scotts_trick wikiPageWikiLink Order_type.
- Scotts_trick wikiPageWikiLink Ordinal_number.
- Scotts_trick wikiPageWikiLink Proper_class.
- Scotts_trick wikiPageWikiLink Rank_of_a_set.
- Scotts_trick wikiPageWikiLink Set_theory.
- Scotts_trick wikiPageWikiLink Total_order.
- Scotts_trick wikiPageWikiLink Ultrapower.
- Scotts_trick wikiPageWikiLink Ultraproduct.
- Scotts_trick wikiPageWikiLink Von_Neumann_universe.
- Scotts_trick wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Scotts_trick wikiPageWikiLinkText "Scott's trick".
- Scotts_trick authorlink "Dana Scott".
- Scotts_trick first "Dana".
- Scotts_trick hasPhotoCollection Scotts_trick.
- Scotts_trick last "Scott".
- Scotts_trick wikiPageUsesTemplate Template:Citation.
- Scotts_trick wikiPageUsesTemplate Template:Harvs.
- Scotts_trick year "1955".
- Scotts_trick subject Category:Set_theory.
- Scotts_trick hypernym Method.
- Scotts_trick type Software.
- Scotts_trick comment "In set theory, Scott's trick is a method for giving a definition of equivalence classes for equivalence relations on a proper class (Jech 2003:65). The method relies on the axiom of regularity but not on the axiom of choice. It can be used to define representatives for ordinal numbers in ZF, Zermelo–Fraenkel set theory without the axiom of choice (Forster 2003:182).".
- Scotts_trick label "Scott's trick".
- Scotts_trick sameAs m.05p4smr.
- Scotts_trick sameAs Q7435833.
- Scotts_trick sameAs Q7435833.
- Scotts_trick wasDerivedFrom Scotts_trickoldid=676383546.
- Scotts_trick isPrimaryTopicOf Scotts_trick.