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- Realizability abstract "In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula. There are many variations of realizability; exactly which class of formulas is studied and which objects are realizers differ from one variation to another. Realizability can be seen as a formalization of the BHK interpretation of intuitionistic logic; in realizability the notion of "proof" (which is left undefined in the BHK interpretation) is replaced with a formal notion of "realizer". Most variants of realizability begin with a theorem that any statement that is provable in the formal system being studied is realizable. The realizer, however, usually gives more information about the formula than a formal proof would directly provide. Beyond giving insight into intuitionistic provability, realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to extract programs from proofs, as in proof mining. It is also related to topos theory via the realizability topos.".
- Realizability wikiPageExternalLink relmrr.ps.gz.
- Realizability wikiPageExternalLink realizability.html.
- Realizability wikiPageExternalLink history.ps.gz.
- Realizability wikiPageID "11009758".
- Realizability wikiPageRevisionID "600141308".
- Realizability hasPhotoCollection Realizability.
- Realizability subject Category:Constructivism_(mathematics).
- Realizability subject Category:Proof_theory.
- Realizability comment "In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula. There are many variations of realizability; exactly which class of formulas is studied and which objects are realizers differ from one variation to another.".
- Realizability label "Realizabilidade".
- Realizability label "Realizability".
- Realizability label "Réalisabilité".
- Realizability label "可实现性".
- Realizability sameAs Réalisabilité.
- Realizability sameAs Realizabilidade.
- Realizability sameAs m.02qx_c1.
- Realizability sameAs Q3454417.
- Realizability sameAs Q3454417.
- Realizability wasDerivedFrom Realizability?oldid=600141308.
- Realizability isPrimaryTopicOf Realizability.