Abbreviation: PeirceA

A \emph{Peirce algebra} is a 2-sorted structure $\mathbf{A}=\langle \mathbf R,\mathbf B,^c\rangle$ such that

$\mathbf R=\langle R,\vee,0,\wedge,1,\neg,\circ,^\smile,e\rangle$ is a relation algebra

$\mathbf B=\langle B,\vee,0,\wedge,1,\neg,f_r\ (r\in R)\rangle$ is a Boolean module over $\mathbf R$

$^c:B\to R$ is \emph{cylindrification}: $f_{x^c}(1)=x$ and $f_r(1)^c=f_r(1)$

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It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.

Let $\mathbf{A}$ and $\mathbf{B}$ be … . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \ldots y)=h(x) \ldots h(y)$

An \emph{…} is a structure $\mathbf{A}=\langle A,\ldots\rangle$ of type $\langle …\rangle$ such that

$\ldots$ is …: $axiom$

$\ldots$ is …: $axiom$

Example 1:

Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.

$\begin{array}{lr}

f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\

\end{array}$ $\begin{array}{lr}

f(6)= &\\
f(7)= &\\
f(8)= &\\
f(9)= &\\
f(10)= &\\

\end{array}$

[[...]] subvariety

[[...]] expansion

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[[...]] subreduct