Structure of Quasivariety Lattices. I. Independent Axiomatizability
- 24 Downloads
We find a sufficient condition for a quasivariety K to have continuum many subquasivarieties that have no independent quasi-equational bases relative to K but have ω-independent quasi-equational bases relative to K. This condition also implies that K is Q-universal.
Keywordsindependent basis quasi-identity quasivariety quasivariety lattice Q-universality
Unable to display preview. Download preview PDF.
- 1.G. Birkhoff, “Universal algebra,” Proc. of the First Canadian Mathematical Congress (Montreal, 1945), Univ. of Toronto, Toronto (1946), pp. 310-326.Google Scholar
- 2.A. I. Mal’tsev, “Borderline problems of algebra and logic,” Proc. of the Int. Math. Congress (Moscow, 1966), Mir, Moscow (1968), pp. 217-231.Google Scholar
- 8.S. V. Sizyĭ, “Quasivarieties of graphs,” Sib. Math. J., 35, No. 4, 783-794 (1994).Google Scholar
- 9.M. V. Sapir, “The lattice of quasivarieties of semigroups,” Alg. Univ., 21, Nos. 2/3, 172-180 (1985).Google Scholar
- 10.M. E. Adams and W. Dziobiak, “Q-universal quasivarieties of algebras,” Proc. Am. Math. Soc., 120, No. 4, 1053-1059 (1994).Google Scholar
- 11.W. Dziobiak, “On lattice identities satisfied in subquasivariety lattices of varieties of modular lattices,” Alg. Univ., 22, Nos. 2/3, 205-214 (1986).Google Scholar
- 12.V. A. Gorbunov, “Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. II,” Algebra and Logic, 34, No. 4, 203-218 (1995).Google Scholar
- 13.V. A. Gorbunov, Algebraic Theory of Quasivarieties, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999).Google Scholar
- 14.M. E. Adams and W. Dziobiak, “Finite-to-finite universal quasivarieties are Q-universal,” Alg. Univ., 46, Nos. 1/2, 253-283 (2001).Google Scholar
- 15.A. M. Nurakunov, “Unreasonable lattices of quasivarieties,” Int. J. Alg. Comput., 22, No. 3 (2012), p. No. 1250006.Google Scholar
- 18.S. M. Lutsak, “On complexity of quasivariety lattices,” Sib. El. Mat. Izv., 14, 92-74 (2017); http://semr.math.nsc.ru/v14/p92-97.pdf.
- 20.A. Tarski, “Equational logic and equational theories of algebras,” in Contributions to Mathematical Logic (Proc. Logic Colloq., Hannover, 1966), North Holland, Amsterdam (1968), pp. 275-288.Google Scholar
- 21.A. V. Kravchenko, A. M. Nurakunov, and M. V. Schwidefsky, “Structure of quasivariety lattices. II. Undecidable problems,” to appear in Algebra and Logic.Google Scholar
- 22.A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).Google Scholar
- 24.W. Dziobiak, “Selected topics in quasivarieties of algebraic systems,” manuscript of the lecture notes delivered at the Workshop on Comput. Algebra and Appl. to Semigroup Theory (the Center of Algebra of Lisbon Univ., Portugal, November 17-21, 1997).Google Scholar