Sh:291

• Mekler, A. H., Nelson, E. M., & Shelah, S. (1993). A variety with solvable, but not uniformly solvable, word problem. Proc. London Math. Soc. (3), 66(2), 225–256. arXiv: math/9301203 DOI: 10.1112/plms/s3-66.2.225 MR: 1199065
• Abstract:
  In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if there is an algorithm which given a finite presentation produces an algorithm for solving the word problem of the algebra so presented. A variety is given with finitely many axioms having a decidable, but not uniformly decidable, word problem. Other related examples are given as well.
• Version 1995-09-04_10 (44p) published version (32p)

@article{Sh:291,
 author = {Mekler, Alan H. and Nelson, Evelyn M. and Shelah, Saharon},
 title = {{A variety with solvable, but not uniformly solvable, word problem}},
 journal = {Proc. London Math. Soc. (3)},
 fjournal = {Proceedings of the London Mathematical Society. Third Series},
 volume = {66},
 number = {2},
 year = {1993},
 pages = {225--256},
 issn = {0024-6115},
 mrnumber = {1199065},
 mrclass = {03B25 (03D40 08A50)},
 doi = {10.1112/plms/s3-66.2.225},
 note = {\href{https://arxiv.org/abs/math/9301203}{arXiv: math/9301203}},
 arxiv_number = {math/9301203}
}