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- Inductive_set abstract "Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ1n formula, for some natural number n, together with a real parameter.The inductive sets form a boldface pointclass; that is, they are closed under continuous preimages. In the Wadge hierarchy, they lie above the projective sets and below the sets in L(R). Assuming sufficient determinacy, the class of inductive sets has the scale property and thus the prewellordering property.".
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- Inductive_set wikiPageOutDegree "16".
- Inductive_set wikiPageRevisionID "607144947".
- Inductive_set wikiPageWikiLink Boldface_pointclass.
- Inductive_set wikiPageWikiLink Category:Descriptive_set_theory.
- Inductive_set wikiPageWikiLink Continuous_function.
- Inductive_set wikiPageWikiLink Descriptive_set_theory.
- Inductive_set wikiPageWikiLink Determinacy.
- Inductive_set wikiPageWikiLink Image_(mathematics).
- Inductive_set wikiPageWikiLink L(R).
- Inductive_set wikiPageWikiLink Pointclass.
- Inductive_set wikiPageWikiLink Polish_space.
- Inductive_set wikiPageWikiLink Preimage.
- Inductive_set wikiPageWikiLink Prewellordering.
- Inductive_set wikiPageWikiLink Prewellordering_property.
- Inductive_set wikiPageWikiLink Projective_hierarchy.
- Inductive_set wikiPageWikiLink Projective_set.
- Inductive_set wikiPageWikiLink Real_number.
- Inductive_set wikiPageWikiLink Scale_(descriptive_set_theory).
- Inductive_set wikiPageWikiLink Scale_property.
- Inductive_set wikiPageWikiLink Subset.
- Inductive_set wikiPageWikiLink Wadge_hierarchy.
- Inductive_set wikiPageWikiLink Zorns_lemma.
- Inductive_set wikiPageWikiLinkText "Inductive set".
- Inductive_set hasPhotoCollection Inductive_set.
- Inductive_set wikiPageUsesTemplate Template:About.
- Inductive_set wikiPageUsesTemplate Template:Cite_book.
- Inductive_set wikiPageUsesTemplate Template:No_footnotes.
- Inductive_set wikiPageUsesTemplate Template:Settheory-stub.
- Inductive_set subject Category:Descriptive_set_theory.
- Inductive_set type Article.
- Inductive_set type Article.
- Inductive_set comment "Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ1n formula, for some natural number n, together with a real parameter.The inductive sets form a boldface pointclass; that is, they are closed under continuous preimages. ".
- Inductive_set label "Inductive set".
- Inductive_set sameAs m.07nwsv.
- Inductive_set sameAs Q6027321.
- Inductive_set sameAs Q6027321.
- Inductive_set wasDerivedFrom Inductive_set?oldid=607144947.
- Inductive_set isPrimaryTopicOf Inductive_set.