Abstract

Dedicated, by her co-authors, to the memory of Evelyn Nelson who died after the paper was submitted Dedicated by Saharon Shelah to his friend Alan Mekler 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. The following two options occur in the literature for what is meant by the solvability of the word problem for a variety V: (1) there is an algorithm which, given a finite presentation 9 * in finitely many generators and relations, solves the word problem for 9 relative to the

Citations