Albert Muchnik

Albert Abramovich Muchnik (1934–2019) 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 recursively enumerable Turing degrees between 0 and 0' . This result, now known as the Friedberg-Muchnik Theorem,[2][3] opened 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 was married to the Russian mathematician Nadezhda Ermolaeva. Their son Andrej, who died in 2007, was also a mathematician working in foundations of mathematics.[5] He died in February 2019.

Selected publications
  • 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
gollark: The fact that there's a meme about it doesn't mean it's *actually* got a high probability of being a problem. And Paradox's question isn't very sensible because of what I said.
gollark: Not really. The actual meme emergence may be random, but the conditions it can persist/replicate in aren't.
gollark: I blame javascript.
gollark: Who consumes lots of them *and* has some "non-masculinity" you can laugh at.
gollark: But "soyboy" is not the same as "person who consumes soy-based products".

References
  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



This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.