I suppose the title is pretty self explanatory.
I have been struggling with the concepts of $K$-free algebras, where $K$ is some class of same-type algebras, over some set $X$. So, in trying to grasp a more intuitive understanding, I am trying to imagine what these $K$-free algebras look like for specific $K$.
In particular, I had an assignment recently talking about the variety of Implication algebras (let's call that $K$ for now). So now I'm wondering what ${\bf F}_K (X)$ is, where $X$ is a set of a finite cardinality (as Burris-Sanka mentions, ${\bf F}_K (X)$ depends essentially on $K$ and $|X|$.
Any ideas, or "intuitive" explanations for $K$-free algebras?