Geodesic
Diophantine representation of enumerable predicates
Izvestiya. Mathematics, Tome 5 (1971) no. 1, pp. 1-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An example is given of a diophantine relation which has exponential growth. This, together with the well-known results of Martin Davis, Hilary Putnam, and Julia Robinson, yields a proof that every enumerable predicate is Diophantine. This theorem implies that Hilbert's tenth problem is algorithmically unsolvable. 
@article{IM2_1971_5_1_a0,
     author = {Yu. V. Matiyasevich},
     title = {Diophantine representation of enumerable predicates},
     journal = {Izvestiya. Mathematics},
     pages = {1--28},
     year = {1971},
     volume = {5},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a0/}
}
TY  - JOUR
AU  - Yu. V. Matiyasevich
TI  - Diophantine representation of enumerable predicates
JO  - Izvestiya. Mathematics
PY  - 1971
SP  - 1
EP  - 28
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a0/
LA  - en
ID  - IM2_1971_5_1_a0
ER  - 
%0 Journal Article
%A Yu. V. Matiyasevich
%T Diophantine representation of enumerable predicates
%J Izvestiya. Mathematics
%D 1971
%P 1-28
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a0/
%G en
%F IM2_1971_5_1_a0
Yu. V. Matiyasevich. Diophantine representation of enumerable predicates. Izvestiya. Mathematics, Tome 5 (1971) no. 1, pp. 1-28. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a0/

[1] Gilbert D., “Matematicheskie problemy”, Problemy Gilberta (II Mezhdunarodnyi kongress matematikov v Parizhe, 8 avgusta 1900 g.), M., 1969

[2] Maltsev A. I., Algoritmy i rekursivnye funktsii, Nauka, M., 1965 | MR

[3] Markov A. A., Teoriya algorifmov, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 42, 1954 | MR | Zbl

[4] Devenport G., Vysshaya arifmetika, Nauka, M., 1965

[5] Devis M., “Arifmeticheskie problemy i rekursivno-perechislimye predikaty”, Matematika, 8:5 (1964), 15–22

[6] Devis M., Putnam X., Robinson Dzh., “Problema razreshimosti dlya pokazatelno-diofantovykh uravnenii”, Matematika, 8:5 (1964), 69–79

[7] Robinson Dzh., “Ekzistentsionalnaya vyrazimost v arifmetike”, Matematika, 8:5 (1964), 3–14

[8] Devis M., “Primeneniya i sledstviya iz poslednei raboty po desyatoi probleme Gilberta”, Matematika, 8:5 (1964), 80–84

[9] Matiyasevich Yu. V., “Diofantovost perechislimykh mnozhestv”, Dokl. AN SSSR, 191:2 (1970), 279–282 | Zbl

[10] Putnam X., “Ob odnoi nerazreshimoi probleme arifmetiki”, Matematika, 8:5 (1964), 55–68