Albert Muchnik

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Albert Abramovich Muchnik (born 1934) is a Russian mathematician who worked in the field of foundations and mathematical logic.

He received his Ph.D from Moscow State Pedagogical Institute in 1959 under the advisorship of Pyotr Novikov.[1] Muchnik's most significant contribution was on the subject of relative computability. He and Richard Friedberg, independently introduced the priority method which gave an affirmative answer to Post's Problem regarding the existence of re Turing degrees between 0 and 0' . This groundbreaking result, now known as the Friedberg-Muchnik Theorem,[2][3] opened a wide study of the Turing degrees of the recursively enumerable sets which turned out to possess a very complicated and non-trivial structure. He also has a significant contribution in the subject of mass problems where he introduced the generalisation of Turing degrees, called "Muchnik degrees" in his work On Strong and Weak Reducibilities of Algorithmic Problems published in 1963.[4] Muchnik also elaborated Kolmogorov's proposal of viewing intuitionism as "calculus of problems" and proved that the lattice of Muchnik degrees is Brouwerian.

Muchnik is married to the Russian mathematician Nadezhda Ermolaeva, and their son Andrej, who died in 2007, was also a mathematician working in foundations of mathematics.[5]

Selected publications[edit]

  • A. A. Muchnik, On the unsolvability of the problem of reducibility in the theory of algorithms. (in Russian) Doklady Akademii Nauk SSSR (N.S.), vol. 108 (1956), pp. 194–197


  1. ^ Albert Abramovich Muchnik, Mathematics Genealogy Project. Accessed January 26, 2010
  2. ^ Robert I. Soare, Recursively Enumberable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. Springer-Verlag, 1999, ISBN 3-540-15299-7; p. 118
  3. ^ Nikolai Vereshchagin, Alexander Shen, Computable functions. American Mathematical Society, 2003, ISBN 0-8218-2732-4; p. 85
  4. ^ A. A. Muchnik, On strong and weak reducibility of algorithmic problems. (Russian) Siberian Mathematical Journal, vol. 4 (1963), pp. 1328–1341
  5. ^ S. I. Adian, A. L. Semenov, V. A. Uspenskii, Andrei Albertovich Muchnik,(in Russian) Uspekhi Matematicheskikh Nauk, vol. 62 (2007), no. 4, pp. 140–144

External links[edit]