ABSTRACT
Let T^ be the term algebra generated by the variables in X under the ope ration -* alone. Let KP^ be the restriction of KP to T^, let be the rela tion of interdeducibility w ith respect to KPd, and let A^ be the class o f all models of R d; the algebras in A d I call d-algebras. My first aim are two characterizations of A^ of which the second is equational:
THEOREM l d A^ is the class of all algebras A = < u (A ), 3> w ith a d is tinguished element e in A which satisfy
and A d is also the class of all algebras A = < u (A ), 3 > de fined by the following set D j of equations
(a0) aDa = bDb (a ^ (a,Da)Da=a (a2) aD(bDc) = (aDb)D(aDc) (ad) (aDb) I) ((bDa)Da) = (bDa) D((aDb)Db) .
