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An algebra A is finitely presented if there is a finite set G of generator symbols, a finite set O of operator symbols, and a finite set Γ of defining relations xΞy where x and y are well-formed terms over G and O, such that A is isomorphic to the free algebra on G and O modulo the congruence induced by Γ.
Dexter Kozen (Sat,) studied this question.
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