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Uniform reducibility of representability problems for algebraic structures

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Given a countable algebraic structure \( \mathfrak{B} \) with no degree we find sufficient conditions for the existence of a countable structure \( \mathfrak{A} \) with the following properties: (1) for every isomorphic copy of \( \mathfrak{A} \) there is an isomorphic copy of \( \mathfrak{A} \) Turing reducible to the former; (2) there is no uniform effective procedure for generating a copy of \( \mathfrak{A} \) given a copy of \( \mathfrak{B} \) even having been enriched with an arbitrary finite tuple of constants.

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Correspondence to I. Sh. Kalimullin.

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Original Russian Text Copyright © 2009 Kalimullin I. Sh.

The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00605) and the President of the Russian Federation (Grant MK-4314.2008.1).


Kazan’. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 334–343, March–April, 2009.

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Kalimullin, I.S. Uniform reducibility of representability problems for algebraic structures. Sib Math J 50, 265–271 (2009). https://doi.org/10.1007/s11202-009-0031-6

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  • computability of an algebraic structure
  • Turing degree
  • mass problem