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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. Yu. Konovalov
AU  - V. E. Plisko
TI  - On Hyperarithmetical Realizability
JO  - Matematičeskie zametki
PY  - 2015
SP  - 725
EP  - 746
VL  - 98
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a6/
LA  - ru
ID  - MZM_2015_98_5_a6
ER  - 
%0 Journal Article
%A A. Yu. Konovalov
%A V. E. Plisko
%T On Hyperarithmetical Realizability
%J Matematičeskie zametki
%D 2015
%P 725-746
%V 98
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a6/
%G ru
%F MZM_2015_98_5_a6
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/

[1] S. C. Kleene, “On the interpretation of intuitionistic number theory”, J. Symbolic Logic, 10 (1945), 109–124 | DOI | MR | Zbl

[2] V. E. Plisko, “Obzor predikatnoi logiki realizuemosti”, Algoritmicheskie voprosy algebry i logiki, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Sergeya Ivanovicha Adyana, Tr. MIAN, 274, MAIK, M., 2011, 222–251 | MR | Zbl

[3] V. E. Plisko, “Rekursivnaya realizuemost i konstruktivnaya logika predikatov”, Dokl. AN SSSR, 214 (1974), 520–523 | MR | Zbl

[4] V. E. Plisko, “Absolyutnaya realizuemost predikatnykh formul”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 315–334 | MR | Zbl

[5] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR | Zbl

[6] S. K. Klini, Vvedenie v metamatematiku, IL, M., 1957 | MR | Zbl

[7] A. Visser, “A propositional logic with explicit fixed points”, Studia Logica, 40:2 (1981), 155–175 | DOI | MR | Zbl

[8] W. Ruitenburg, “Basic predicate calculus”, Notre Dame J. Formal Logic, 39:1 (1998), 18–46 | DOI | MR | Zbl