Генерическая неполнота формальной арифметики

Famous Gödel's incompleteness theorem states that formal arithmetic (if it is consistent) has a statement that is unprovable and incontrovertible by any recursive systems of axioms. In this paper we prove that Gödel's theorem remains true if we restrict the set of all arithmetic statements by some natural subsets of “almost all” statements (so called strongly generic sets).