The existence of a near-unanimity term in a finite algebra is decidable
Miklós Maróti
Source: J. Symbolic Logic Volume 74, Issue 3 (2009), 1001-1014.
Abstract
We prove that it is decidable of a finite algebra whether it has a near-unanimity term operation, which settles a ten-year-old problem. As a consequence, it is decidable of a finite algebra in a congruence distributive variety whether it admits a natural duality.
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158096
Digital Object Identifier: doi:10.2178/jsl/1245158096
References
K. A. Baker and A. F. Pixley, Polynomial interpolation and the Chinese remainder theorem, Mathematische Zeitschrift, vol. 143 (1975), pp. 165--174.
Mathematical Reviews (MathSciNet):
MR371782
Digital Object Identifier: doi:10.1007/BF01187059
A. Bulatov, A. A. Krokhin, and P. Jeavons, Constraint satisfaction problems and finite algebras, Lecture Notes in Computer Science, vol. 1853(2000), pp. 272--282.
Mathematical Reviews (MathSciNet):
MR1795899
Digital Object Identifier: doi:10.1007/3-540-45022-X_24
B. A. Davey, L. Heindorf, and R. McKenzie, Near unanimity: an obstacle to general duality theory, Algebra Universalis, vol. 33 (1995), pp. 428--439.
Mathematical Reviews (MathSciNet):
MR1322784
Digital Object Identifier: doi:10.1007/BF01190710
B. A. Davey and H. Werner, Dualities and equivalences for varieties of algebras, Contributions to Lattice Theory (Szeged, $1980)$, Colloqium Mathematica Societatis János Bolyai, vol. 33, North-Holland, Amsterdam, 1983, pp. 101--275.
Mathematical Reviews (MathSciNet):
MR724265
T. Feder and M. Y. Vardi, The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory, SIAM Journal of Computing, vol. 28 (1998), no. 1, pp. 57--104.
Mathematical Reviews (MathSciNet):
MR1630445
Digital Object Identifier: doi:10.1137/S0097539794266766
P. M. Idziak, P. Marković, R. McKenzie, M. Valeriote, and R. Willard, Tractability and learnability arising from algebras with few subpowers, Proceedings of 22nd Logic in Computer Science, 2007, pp. 213--224.
P. Jeavons, D. Cohen, and M. C. Cooper, Constraints, consistency and closure, Artificial Intelligence, vol. 101 (1998), pp. 251--265.
Mathematical Reviews (MathSciNet):
MR1641467
Digital Object Identifier: doi:10.1016/S0004-3702(98)00022-8
D. Lau, Function algebras on finite sets: Basic course on many-valued logic and clone theory, Monographs in Mathematics, Springer, Berlin Heidelberg, 2006.
Mathematical Reviews (MathSciNet):
MR2254622
L. Lovász, Kneser's conjecture, chromatic numbers and homotopy, Journal of Combinatorial Theory, Series A, vol. 25 (1978), pp. 319--324.
Mathematical Reviews (MathSciNet):
MR514625
Digital Object Identifier: doi:10.1016/0097-3165(78)90022-5
M. Maróti, On the (un)decidability of a near-unanimity term, Algebra Universalis, vol. 57 (2007), no. 2, pp. 215--237.
Mathematical Reviews (MathSciNet):
MR2369181
Digital Object Identifier: doi:10.1007/s00012-007-2037-x
M. Maróti and R. McKenzie, Existence theorems for weakly symmetric operations, Algebra Universalis, vol. 59 (2008), no. 3--4, pp. 463--489.
Mathematical Reviews (MathSciNet):
MR2470592
Digital Object Identifier: doi:10.1007/s00012-008-2122-9
R. McKenzie, Is the presence of a nu-term a decidable property of a finite algebra?, manuscript, October 15, 1997.
