Ершов Ю. Л. Теория нумераций. / Серия: Математическая логика и основания математики.
Москва : Наука. Главная редакция физико-математической литературы, 1977.
416 с. : ил. Твердый издательский переплет, суперобложка, обычный формат. Тираж 7900 экз.
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Ershov, Yuri L. Theory of Numberings (Teoriya numeratsiy). / Series: Mathematical Logic and Foundations of Mathematics (Matematicheskaya logika i osnovaniya matematiki).
Moscow : Nauka. Main Editorial Board of Physico-Mathematical Literature, 1977.
416 pp. : ill. Hardcover, dust jacket, standard format. Print run: 7,900 copies. In Russian.
This 1977 monograph by Academician Yuri Ershov is a foundational text in the field of computability theory and mathematical logic. Published by the "Nauka" publishing house in its specialized series, the book serves as the first systematic exposition of the theory of numberings—a branch of algorithm theory that Ershov himself was instrumental in developing.
The central premise of the theory is the formalization of how abstract mathematical structures (such as groups, rings, or classes of functions) can be represented using natural numbers. By assigning "numbers" to these abstract objects, mathematicians can apply the rigorous tools of recursion theory to non-numerical sets. This allows for a precise definition of what it means for an abstract structure to be "computable" or "effectively given."
The book covers essential topics including the lattice of numberings, computable enumerations, and the application of these concepts to topology and analysis (specifically through the study of f-spaces). Ershov's work provided the theoretical framework necessary for much of modern constructive mathematics and theoretical computer science in the Soviet Union and beyond.
Despite a print run of 7,900 copies, this edition is highly valued by collectors and scholars for its historical importance as the "primary source" for this mathematical discipline. The presence of the original dust jacket is particularly desirable, as it protected the academic binding of one of the most significant logic texts of the late 20th century. For mathematicians, logicians, and historians of science, Ershov’s Theory of Numberings remains an indispensable reference.