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5 votes

Kuratowski's 14 theorem and universal algebra

This is an affirmative answer to the first question. Let $\mathcal{A}$ be any algebra whose fundamental operations are constant. Let $\mathcal{B}\in\mathsf{HSP}(\mathcal{A})$ be any algebra. The ...
Keith Kearnes's user avatar
1 vote

Birkhoff's completeness theorem put into practice

The proof of Birkhoff's theorem, much like the proof of the completeness theorem for predicate logic, will not give a very interesting algorithm for computing a proof for a statement known to be valid:...
stefan.hetzl's user avatar
10 votes

How much choice is needed to prove the completeness of equational logic?

I do not know what proofs precisely you have in mind, but at least for operations with finite arities no choice is needed, nor excluded middle for that matter. Let us review the proof to make sure ...
Andrej Bauer's user avatar
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