Geodesic
On Hyperarithmetical Realizability
Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 725-746

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The notion of hyperarithmetical realizability is introduced for various extensions of the language of formal arithmetic. The correctness of classical, intuitionistic, and basic logic with respect to the semantics based on hyperarithmetical realizability is studied.
Keywords: hyperarithmetical realizability, formal arithmetic, hyperarithmetical set, hyperarithmetical predicate, hyperarithmetical function, Gödel number, universal function. 
@article{MZM_2015_98_5_a6,
     author = {A. Yu. Konovalov and V. E. Plisko},
     title = {On {Hyperarithmetical} {Realizability}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {725--746},
     publisher = {mathdoc},
     volume = {98},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a6/}
}
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A. Yu. Konovalov; V. E. Plisko. On Hyperarithmetical Realizability. Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 725-746. http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a6/