What does realizability mean?

Definitions for realizability
re·al·iz·abil·i·ty

This dictionary definitions page includes all the possible meanings, example usage and translations of the word realizability.

Wiktionary

  1. realizabilitynoun

    The property or characteristic of being realizable.

Wikipedia

  1. Realizability

    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.

Wikidata

  1. Realizability

    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" 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of realizability in Chaldean Numerology is: 5

  2. Pythagorean Numerology

    The numerical value of realizability in Pythagorean Numerology is: 5

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realizability#100000#221080#333333

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"realizability." Definitions.net. STANDS4 LLC, 2024. Web. 17 Jul 2024. <https://www.definitions.net/definition/realizability>.

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