On the Two-Variable Fragment of the Equational Theory of the Max-Sum Algebra of the Natural Numbers
This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the nonexistence of a finite basis for N—a result previously obtained by the authors.
KeywordsPartial Order Equational Theory Axiom System Free Algebra Constant Zero
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