This article is cited in 1 paper

Mathematical logic, algebra and number theory

On the сomplexity of quasivariety lattices

S. M. Lutsak

The L.N. Gumilyov Eurasian National University, Satpaev str. 2, 010000, Astana, Kazahstan

Abstract: We prove that any AD-class of algebraic structures of finite signature contains continuum many proper subclasses, which have the Nurakunov non-computability property, but which are not Q-universal (among those are almost all the known Q-universal quasivarieties nowadays). A similar result holds for some classes of algebraic structures of countable signature. This provides a negative answer to an open question.

Keywords: computable set, lattice, quasivariety, Q-universality.

UDC: 512.56, 512.57

MSC: 06B15, 08C15

Received November 14, 2016, published February 10, 2017

DOI: 10.17377/semi.2017.14.010

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