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Uriy Leonidovich Ershov
Юрий Ершов
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Scientific interests: logic, solvable theories, model theory.
Research centers: Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Additional information about the researcher:
The beginning of Y.L. Ershov’s scientific activity coincided with the rapid development in the 60s of research on the solvability of elementary theories. Having entered this field since his student years, Y.L. Ershov contributed a lot to its further development. He developed powerful
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Scientific interests: logic, solvable theories, model theory.
Research centers: Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Additional information about the researcher:
The beginning of Y.L. Ershov’s scientific activity coincided with the rapid development in the 60s of research on the solvability of elementary theories. Having entered this field since his student years, Y.L. Ershov contributed a lot to its further development. He developed powerful methods of proving the solvability and insolubleness of elementary theories. The outstanding achievement of Y.L. Ershov in this direction was the solution of the classical problem of the solvability of the elementary field theory of p-adic numbers. He also found new series of fields with solvable elementary theory, proved the algorithmic insolvability of the theory of the class of finite symmetric groups and other theories. As a consequence of elementary classification, he proved the solvability of the elementary theory of distributional structures with relative additions and the theory of filters. These, as well as a number of other works, immediately made Y.L. Ershov’s name known among logicians around the world.
In the future, the range of mathematical interests of Y.L. Ershov expands, he receives fundamental results in the theory of algorithms and model theory, in a number of new developing areas of mathematical logic and algebra. Y.L. Ershov is the creator of the general theory of numbering, which has found numerous applications in mathematical logic. This theory provides, in particular, a methodological basis for the study of algorithmic problems of mathematics, as well as the construction of a modern theory of calculations, has a connection with methodological and theoretical issues of programming. Y.L. Ershov owns the fundamental results on the theory of constructive systems - a new scientific direction located at the junction of the theory of solvability and the theory of numbering.
Y.L. Ershov’s works on the development of recursive theory on permissible sets were the basis for the development of a new concept of programming on computers – the concept of semantic programming. In addition, Y.L. Ershov is one of the authors of a new approach to the substantiation of mathematics, developing and modifying the well-known Hilbert program: an approach that connects computability with determinability.
In mathematics, such concepts as the Ershov hierarchy in the theory of algorithms, the ideals and characteristics of Ershov-Tarsky in the theory of Boolean algebras, the language of S-expressions of Ershov in semantic programming, the A-space of Ershov in theoretical programming entered, becoming generally recognized.