The problem of incompleteness in mathematical theory and ontological assumptions for its solution

In this monograph, a series of logical and mathematical surveys of the author, begun in his book “The problem of the incompleteness of theory and its epistemological significance”, published in 1986, was continued. In both cases, the main subject of research is the task of clarifying the philosophical and logical prerequisites of the Gödel theorems of incompleteness. But the approaches to solving the problem are different: in the first case, the epistemological, in the second - ontological.
In the previous work, the existence of a logical connection between incomplete theorems and the ontological status of such mathematical objects as an empty class in the theory of sets was demonstrated. This made it possible to resolve the well -known Antinomy of Russell. Subsequently, it was found that all pure (not applied) mathematics is ontological in the sense of fundamental ontology of Martin Heidegger. Within the framework of this ontology, an operation of dialectical denial (prison) was established, which made it possible to create complementary-dialectic logic.
The book is recommended for a wide range of readers familiar with elementary logic and interested in increasing their creative potential