Stone algebras

Abbreviation: StAlg

Definition

A 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

$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &1\\ f(4)= &2\\ f(5)= &2\\ f(6)= &4\\ f(7)= &5\\ f(8)= &10\\ f(9)= &16\\ f(10)= &28\\ \end{array}$

Subclasses

Superclasses

References