On neat reducts of algebras of logic
Studia Logica 68 (2):229-262 (2001)
| Abstract | SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if and only if > 1.From this it easily follows that for 1 , the operation of forming -neat reducts of algebras in K does not commute with forming subalgebras, a notion to be made precise | |||||||||
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