Algebraic completeness results for sKD and its Extensions

This paper investigates algebraic semantics for sKD and its extensions $sKD_\triangle$, $sKD\forall$, and $sKD\forall{_\triangle}$: sKD is a variant of the infinite -valued Kleene- Diense logic KD; $sKD_\triangle$ is the sKD with the Baaz's projection A; and $sKD\forall$ and $sKD\forall{_\triangle}$: are the first order extensions of sKD and $sKD_\triangle$, respectively. I first provide algebraic completeness for each of sKD and $sKD_\triangle$. Next I show that each $sKD\forall$ and $sKD\forall{_\triangle}$: is algebraically complete.