On BCK Algebras – Part III: Classes of Examples of Proper MVAlgebras, BLAlgebras and Divisible Bounded Residuated Lattices, with or without Condition (WNM)
In this paper, Part III, we shall illustrate by classes of finite examples the close connections between MValgebras, by one side, and BL algebras and divisible bounded residuated lattices, on the other side; we present classes of examples of proper MV algebras, BL algebras and divisible bounded residuated lattices, satisfying or not satisfying condition Weak Nilpotent Minimum (WNM). We use equivalent definitions of these algebras, as particular cases of reversed left-BCK algebras, as established in Part I.
Keywords: MV algebra, Wajsberg algebra, BCK algebra, bounded BCK(P) lattice, bounded residuated lattice, BL algebra, Hájek(P) algebra, divisible bounded BCK(P) lattice, Heyting algebra.
AMS classification (2000): 03G25, 06F05, 06F35