Sheinfinkel, Moses Elievich

Moses Sheinfinkel was born in Yekaterinoslav in the family of the merchant of the first guild Ilya Girshevich Sheinfinkel, who, on February 22, 1894, together with another Ekaterinoslav merchant Aron Gertsevich Lurie founded the Lurie and Scheinfinkel trading house engaged in grocery trade ^{[3] [4] [5]} .

He studied at Novorossiysk University in Odessa , studying mathematics under the leadership of Samuil Osipovich Shatunovsky (1859-1929), who worked in the field of geometry and the foundations of mathematics . From 1914 to 1924 he trained at the University of Gottingen under the leadership of David Hilbert ^[6] . On December 7, 1920, speaking to colleagues, he outlined the concept of combinatorial logic . His report, published in 1924 by Heinrich Behmann ( German: Heinrich Behmann ), laid the foundation for the research of Curry and Church in the field of the foundations of mathematics ^[7] . Leaving Göttingen, in the mid-1920s, Scheinfinkel moved to Moscow, but he could no longer engage in scientific activities as before ^[8] .

In 1927 he was recognized as mentally ill and placed in a psychiatric hospital ^{[7] [9]} . Information about exactly what the scientist was sick with and why the disease developed did not survive. His subsequent life passed in poverty, and he died in Moscow, approximately in 1942 (the exact date of his death is not known). His working papers were started by the neighbors for kindling ^[9] .

In 1929, another work by Sheinfinkel was published, prepared for publication by Paul Bernays . In it, Scheinfinkel proposed a solution to the problem of resolution for some special cases of formulas of narrow predicate calculus; first pointed out a system of axioms sufficient to deduce all identically true implicative formulas, known as the Bernays – Schönfinkel class ^[10] .

Scheinfinkel developed a formal system that avoids the use of related variables. His system was essentially equivalent to combinatorial logic based on combinators B , C , I , K, and S. Scheinfinkel was able to show that the system can be reduced only to K and S , and to state the proof that such a variant of the system is as complete as the predicate logic ^[7] .

His work also showed that functions of two or more arguments can be replaced by a function that takes only one argument. The mechanism of such a replacement simplifies the work both in terms of combinatorial logic and lambda calculus and was later called currying , in honor of Haskell Curry .

• Über die Bausteine ​​der mathematischen Logik, Mathematische Annalen 92 , pp. 305–316, 1924. Stefan Bauer-Mengelberg translated this article as “On the building blocks of mathematical logic” in Jean van Heijenoort , 1967. A Source Book in Mathematical Logic, 1879-1931 . Cambridge : Harvard University Press, pp. 355-366.
• Zum Entscheidungsproblem der mathematischen Logik (with Paul Bernays ), Mathematische Annalen 99 : 342–372, 1929.

• Grossman Leonid. Mathematical Odessa . - Odessa: "Optimum", 2011. - 131 p. - ISBN 978-966-344-411-6 .
• Sergey Tropanets “Moses Sheinfinkel and Combinatorial Language”