Geodesic
Absolute realizability of predicate formulas
Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 291-308.

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

The concept of an absolutely realizable predicate formula is introduced. It can be regarded as a certain refinement of the concept of a constructively generally valid formula in predicate logic. It is proved that the class of all absolutely realizable formulas is a $\Pi^1_1$-complete set. Bibliography: 16 titles. 
@article{IM2_1984_22_2_a5,
     author = {V. E. Plisko},
     title = {Absolute realizability of predicate formulas},
     journal = {Izvestiya. Mathematics },
     pages = {291--308},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a5/}
}
TY  - JOUR
AU  - V. E. Plisko
TI  - Absolute realizability of predicate formulas
JO  - Izvestiya. Mathematics 
PY  - 1984
SP  - 291
EP  - 308
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a5/
LA  - en
ID  - IM2_1984_22_2_a5
ER  - 
%0 Journal Article
%A V. E. Plisko
%T Absolute realizability of predicate formulas
%J Izvestiya. Mathematics 
%D 1984
%P 291-308
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a5/
%G en
%F IM2_1984_22_2_a5
V. E. Plisko. Absolute realizability of predicate formulas. Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 291-308. http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a5/

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

[2] Klini S. K., Vvedenie v metamatematiku, IL, M., 1957

[3] Novikov P. S., Konstruktivnaya matematicheskaya logika s tochki zreniya klassicheskoi, Nauka, M., 1977 | MR

[4] Kipnis M. M., “O realizatsiyakh predikatnykh formul”, Zapiski nauchnykh seminarov Leningr. otd. Matem. in-ta AN SSSR, 20, 1971, 40–48 | MR | Zbl

[5] Plisko V. E., “Nearifmetichnost klassa realizuemykh predikatnykh formul”, Izv. AN SSSR. Ser. matem., 41:3 (1977), 483–502 | MR | Zbl

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

[7] Plisko V. E., “Ob interpretatsiyakh predikatnykh formul, svyazannykh s konstruktivnoi logikoi”, Tretya Vsesoyuzn. konfer. po matematicheskoi logike, tez. dokl., Novosibirsk, 1974, 170–172

[8] Plisko V. E., “Nekotorye varianty ponyatiya realizuemosti dlya predikatnykh formul”, Dokl. AN SSSR, 226:1 (1976), 61–64 | MR | Zbl

[9] Skvortsov D. P., “Dva obobscheniya ponyatiya finitnoi zadachi”, Issledovaniya po neklassicheskim logikam i teorii mnozhestv, 1979, 201–240, M. | MR

[10] Plisko V. E., “Nekotorye varianty ponyatiya realizuemosti dlya predikatnykh formul”, Izv. AN SSSR. Ser. matem., 42:3 (1978), 636–653 | MR

[11] Nelson D., “Recursive functions and intuitionistic number theory”, Trans. Amer. Math. Soc., 61 (1947), 307–368 | DOI | MR

[12] Rose G. F., “Propositional calculus and realizability”, Trans. Amer. Math. Soc., 75 (1953), 1–19 | DOI | MR | Zbl

[13] Varpakhovskii F. L., “O nerealizuemosti diz'yunktsii nerealizuemykh formul”, Dokl. AN SSSR, 161:6 (1965), 1257–1258 | Zbl

[14] Kipnis M. M., “Ob odnom svoistve propozitsionalnykh formul”, Dokl. AN SSSR, 174:2 (1967), 277–278 | MR | Zbl

[15] Orevkov V. P., “Svyaz konstruktivnoi obscheznachimosti s vyvodimostyu v klassicheskom ischislenii predikatov”, Vsesoyuzn. simpozium po matematicheskoi logike, tez. dokl., Alma-Ata, 1965, 35

[16] Rodzhers X., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR