A variety with solvable, but not uniformly solvable, word problem
Logic
2016-09-06 v1 Rings and Algebras
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.
Cite
@article{arxiv.math/9301203,
title = {A variety with solvable, but not uniformly solvable, word problem},
author = {Alan H. Mekler and Evelyn Nelson and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9301203},
year = {2016}
}