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- Bar_induction abstract "Bar induction is a reasoning principle used in intuitionistic mathematics, introduced by L.E.J. Brouwer.It is useful in giving constructive versions of classical results.It is based on an inductive argument.The goal of the principle is to prove properties of infinite streams of natural numbers, called choice sequences in intuitionistic terminology, by inductively reducing them to decidable properties of finite lists.Given two predicates R and S on finite lists of natural numbers such that the following conditions hold: R is decidable; every choice sequence has a finite prefix satisfying R (this is expressed by saying that R is a bar); every list satisfying R also satisfies S; if all extensions of a list by one element satisfy S, then that list also satisfies S;then we can conclude that S holds for the empty list.In classical reverse mathematics, \"bar induction\" (BI) denotes the related principle stating that if a relation R is a well-order, then we have the schema of transfinite induction over R for arbitrary formulas.".
- Bar_induction wikiPageID "5492505".
- Bar_induction wikiPageLength "1800".
- Bar_induction wikiPageOutDegree "11".
- Bar_induction wikiPageRevisionID "691558724".
- Bar_induction wikiPageWikiLink Anne_Sjerp_Troelstra.
- Bar_induction wikiPageWikiLink Category:Constructivism_(mathematics).
- Bar_induction wikiPageWikiLink Category:Mathematical_induction.
- Bar_induction wikiPageWikiLink Choice_sequence.
- Bar_induction wikiPageWikiLink Classical_logic.
- Bar_induction wikiPageWikiLink Intuitionism.
- Bar_induction wikiPageWikiLink L._E._J._Brouwer.
- Bar_induction wikiPageWikiLink Michael_Dummett.
- Bar_induction wikiPageWikiLink Reverse_mathematics.
- Bar_induction wikiPageWikiLink Stephen_Cole_Kleene.
- Bar_induction wikiPageWikiLink Transfinite_induction.
- Bar_induction wikiPageWikiLinkText "bar induction".
- Bar_induction first "A.G.".
- Bar_induction id "Bar_induction".
- Bar_induction last "Dragalin".
- Bar_induction oldid "12849".
- Bar_induction title "Bar induction".
- Bar_induction wikiPageUsesTemplate Template:Logic-stub.
- Bar_induction wikiPageUsesTemplate Template:SpringerEOM.
- Bar_induction subject Category:Constructivism_(mathematics).
- Bar_induction subject Category:Mathematical_induction.
- Bar_induction hypernym Principle.
- Bar_induction type Agent.
- Bar_induction type Proof.
- Bar_induction type Theory.
- Bar_induction comment "Bar induction is a reasoning principle used in intuitionistic mathematics, introduced by L.E.J.".
- Bar_induction label "Bar induction".
- Bar_induction sameAs Q4857985.
- Bar_induction sameAs m.0dp6rr.
- Bar_induction sameAs Q4857985.
- Bar_induction wasDerivedFrom Bar_induction?oldid=691558724.
- Bar_induction isPrimaryTopicOf Bar_induction.