### A variety with solvable, but not uniformly solvable, word problem

by Mekler and Nelson and Shelah. [MNSh:291]

Proc London Math Soc, 1993

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.

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