0. Examples

(1) A group $\langle G; \cdot, \ ^ {-1}, e \rangle$.

(2) A ring $\langle R; +, \cdot , -, 0 \rangle$; or a ring with 1 $\langle R; +, \cdot , -, 0, 1 \rangle$.

(3) A Boolean algebra $\langle$   B$; \vee , \wedge , 0, 1, ' \rangle$.

(4) A lattice $\langle L ; \vee , \wedge \rangle$; the lattice $\langle$   R$; \max, \min \rangle$.

(5) A vector space $\langle V; +, -, 0,$   mult by $r$    for each $r \in$   R$\rangle$ (if $V$ is over the reals).

(6) Perkins' semigroup $\langle S; \cdot \rangle$, with elements

$\left[\begin{array}{cc}0&0\\ 0&0\end{array}\right]$, $\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right]$, $\left[\begin{array}{cc}1&0\\ 0&0\end{array}\right]$, $\left[\begin{array}{cc}0&0\\ 0&1\end{array}\right]$, $\left[\begin{array}{cc}0&1\\ 0&0\end{array}\right]$, $\left[\begin{array}{cc}0&0\\ 1&0\end{array}\right]$.

(7) The 1-unary algebra $\langle A; f \rangle$ with diagram $\parbox{1in}{\includegraphics{text/Adir/1-unary.eps}}$

(8) The tournament $\langle T; \vee, \wedge \rangle$ with diagram $\parbox{1in}{\includegraphics{text/Adir/tournament.eps}}$

(9) The Heyting algebra $\langle \{0,a,1\}; \vee, \wedge, \rightarrow , 0, 1 \rangle$.

(10) The Murskii 1-binary algebra $\langle M; \cdot \rangle$ with table

	0	a	b
0	0	0	0
a	0	0	a
b	0	b	b

(11) Tarski's high-school-algebra algebra $\langle \omega; +, \cdot , \uparrow , 1 \rangle$.

(12) Shallon's graph algebra $\langle G \cup \{0\} ; \cdot \rangle$, $G =$ $\parbox{1in}{\includegraphics{text/Adir/shallon.eps}}$

(13) The relation algebra $\langle$   Pow$(S \times S); \cup, \cap, \emptyset, 1, ', \circ, \ ^ {\cup}, \Delta \rangle$ ($S$ any set).

(14) The implication algebra $\langle$   2$; \rightarrow \rangle$.

(15) The lattice-ordered group $\langle$   Z$; \wedge, \vee, +, -, 0 \rangle$.

(16) The set algebra $\langle S; \rangle$ (set $S$ with no operations).

(17) The 1-binary algebra $\langle \{0,1,2\};\cdot \rangle$ with table

	0	1	2
0	0	2	1
1	1	0	2
2	2	1	0