Tarski's finite basis problem is undecidable

International Journal of Algebra and Computation

Volumn 6, Issue 1, 1996, Pages 49-104

  McKenzie, Ralph ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030531448     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196796000040     Document Type: Article

References (23)

1. K. Baker, Finite equational bases for finite algebras in a congruence-distributive equational class, Adv. in Math. 24 (1977), 207-243.
2. K. Baker, G. McNulty, H. Werner, The finitely based varieties of graph algebras, Acta Scient. Math. (Szeged) 51 (1987), 3-15.
3. K. Baker, G. McNulty, H. Werner, Shift-automorphism methods for inherently nonfinitely based varieties of algebras, Czech. Math. J. 39 (1989), 53-69.
4. B. Jónsson, Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110-121.
5. S. C. Kleene, Introduction to Metamathematics, D. Van Nostrand Co., Inc., 1950.
6. R. C. Lyndon, Identities in finite algebras, Proc. Amer. Math. Soc. 5 (1954), 8-9.
7. R. McKenzie, A new product of algebras and a type reduction theorem, Algebra Universalis 18 (1984), 29-69.
8. R. McKenzie, Finite equational bases for congruence modular varieties, Algebra Universalis 24 (1987), 224-250.
9. R. McKenzie, The residual bounds of finite algebras, this volume.
10. R. McKenzie, The residual bound of a finite algebra is not computable, this volume.
11. R. McKenzie, Residual smallness relativized to congruence types, in progress.
12. G. McNulty, The decision problem for equational bases of algebras, Annals of Math. Logic 11 (1977), 193-259.
13. G. McNulty, A field guide to equational logic, J. Symbolic Computation 14 (1992), 371-397.
14. G. McNulty, C. Shallon, Inherently nonfinitely based finite algebras, in: Universal Algebra and Lattice Theory, Lecture Notes in Mathematics, vol. 1004, R. Freese and O. Garcia, eds., pp. 206-231, Springer-Verlag, 1983.
15. V. L. Murskiǐ, The number of k-element algebras with a binary operation which do not have a finite basis of identities, (Russian) Problemy Kibernet. 35 (1979), 5-27.
16. S. Oates MacDonald, M. R. Vaughan-Lee, Varieties that make one cross, J. Austral. Math. Soc. (Series A) 26 (1978), 368-382.
17. P. Perkins, Unsolvable problems for equational theories, Notre Dame J. Formal Logic 8 (1967), 175-185.
18. P. Perkins, Bases for equational theories of semigroups, J. of Algebra 11 (1969), 298-314.
19. P. Perkins, Basis questions for general algebras, Algebra Universalis 19 (1984), 16-23.
20. P. Perkins, Finite axiomatizability for equational theories of computable groupoids, Journal of Symbolic Logic 54 (1989), 1018-1022.
21. M. V. Sapir, Problems of Burnside type and the finite basis property in varieties of semigroups, Math. USSR - Izv. 30 (1988a), 295-314.
22. M. V. Sapir, Inherently nonfinitely based finite semigroups, Math. USSR - Sb. 61 (1988b), 155-166.
23. A. Tarski, Equational logic and equational theories of algebras, in: Contributions to Mathematical Logic: Proceedings of the Logic Colloquium, Hanover 1966, H. A. Schmidt, K. Schütte, H. J. Thiele, Editors. Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, 1968, pp. 275-288.