Генерическая неразрешимость экзистенциальной теории кольца целых чисел

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).