Three-element non-finitely axiomatizable matrices and term-equivalence
DOI:
https://doi.org/10.12775/LLP.2014.010Keywords
matrix, term-equivalence, finite axiomatizatonAbstract
It was shown in [5] that all two-element matrices are finitely based independently of their classification by term equivalence (the Post classification). In particular, each 2-valued matrix is finitely axiomatizable. We show below that for certain two not finitely axiomatizable 3-valued matrices this property is also preserved under term equivalence. The general problem, whether finite axiomatizability of a finite matrix is preserved under term-equivalence, is still open, as well as the related problem as to whether the consequence operation of a finite matrix is finitely based.References
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