Geodesic
Generic undecidability of existential theory of integer numbers ring
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 882-887

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Famous theorem of Matiyasevich about undecidability of Hilbert’s thenth problem implies that existential theory of ring of integer numbers is undecidable. In this paper we prove that this theory remains undecidable if we restrict the set of all existential arithmetic statements by any recursive subsets of almost all statements (so called generic sets).
Keywords: existential theory of ring of integer numbers, generic complexity. 
@article{SEMR_2016_13_a24,
     author = {A. N. Rybalov},
     title = {Generic undecidability of existential theory of integer numbers ring},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {882--887},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a24/}
}
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A. N. Rybalov. Generic undecidability of existential theory of integer numbers ring. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 882-887. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a24/