I asked long ago whether the class $C$ of free monoids is a first-order axiomatizable class. The answer was no. However, the class $C$ does have an associated first-order theory $Th(C)$. Is that theory finitely axiomatizable? If so, what additional axioms do we need to add to the axioms for monoids to axiomatize that theory?
2026-03-26 16:10:21.1774541421
Is the first-order theory of the class of free monoids finitely axiomatizable?
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