Table of Contents
Stone algebras
Abbreviation: StAlg
Definition
A \emph{Stone algebra} is a distributive p-algebra $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle $ such that
$(x^*)^*\vee x^* =1$, $0^*=1$
Morphisms
Let $\mathbf{L}$ and $\mathbf{M}$ be Stone algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0 $, $h(1)=1$, $h(x^*)=h(x)^*$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr}
f(1)= &1
f(2)= &1
f(3)= &1
f(4)= &2
f(5)= &2
f(6)= &4
f(7)= &5
f(8)= &10
f(9)= &16
f(10)= &28
\end{array}$
