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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…

Applications, Later developments & Use in proof mining

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Later developments

Use in proof mining

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Realizability

Nodes26
Edges25
Triples49
Avg. degree1.92
Density0.076923
Components1

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Realizability

Top relations

related to References · 34
Realizability → American Mathematical Society, An Historical Essay, Analysis, August, Berlin, Birkedal, Cambridge Summer School, Cambridge/England, Constructive Functionals, Constructivity, Finite Types, Hartley Rogers, Heyting, Interpretation, ISBN, Jaap, Journal, JSTOR, Kleene, Kreisel
related to Example: Kleene's 1945-realizability · 5
Realizability → Any, Heyting, Kleene's, The, Thus
related to Later developments · 5
Realizability → Kreisel, Markov's, Modified, On, Relative
is a · 2
Realizability → collection of methods in proof theory used to study constructive proofs and extract additional information from them, intuitionist analysis of computable or computably enumerable elements of data structures that are not necessarily computable
related to Use in proof mining · 2
Realizability → Program, Rocq

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Important terminology

formula realizer proof theory realizes logic formal formulas realizers interpretation intuitionistic number thus used computable pair mathematical one heyting proofs

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Realizabilityis acollection of methods in proof theory used to study constructive proofs and extract additional information from them0.90text
Realizabilityis aintuitionist analysis of computable or computably enumerable elements of data structures that are not necessarily computable0.90text
Rocqinstance ofProgram extraction using realizability is implemented in some proof assistants0.80text
Realizabilityrelated to Example: Kleene's 1945-realizabilityKleene's0.60section
Realizabilityrelated to Example: Kleene's 1945-realizabilityHeyting0.60section
Realizabilityrelated to Example: Kleene's 1945-realizabilityThe0.60section
Realizabilityrelated to Example: Kleene's 1945-realizabilityAny0.60section
Realizabilityrelated to Example: Kleene's 1945-realizabilityThus0.60section
Realizabilityrelated to Later developmentsKreisel0.60section
Realizabilityrelated to Later developmentsModified0.60section
Realizabilityrelated to Later developmentsMarkov's0.60section
Realizabilityrelated to Later developmentsOn0.60section

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