Abbreviation: TarskiA

A \emph{Tarski algebra} is a structure $\mathbf{A}=\langle A,\to\rangle$ of type $\langle 2\rangle$ such that $\to$ satisfies the following identities:

$(x\to y)\to x=x$

$(x\to y)\to y=(y\to x)\to x$

$x\to(y\to z)=y\to(x\to z)$

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

Example 1: $\langle\{0,1\},\to\rangle$ where $x\to y=0$ iff $x=1$ and $y=0$.

Tarski algebras are the implication subreducts of Boolean algebras.

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

[[...]] supervariety

[[...]] subreduct