Expansion by a new constant may change the finite axiomatization property of a matrix
Katarzyna Pałasińska · Repozytorium Politechniki Krakowskiej · 2016
We give an example of a finite matrix with the property that expanding its language with a constant changes its finite axiomatization property: in the language with one binary operation the tautologies of the matrix are finitely axiomatizable while in the expanded language they are not. The constant we add is not definable in the original language.The deductive system generated by this matrix is not algebraizable.