Axiome, Modelle, Theorien

A	=	$\displaystyle \forall$ x : f (a, x) = x $\displaystyle \wedge$ f (x, a) = x
	$\displaystyle \wedge$	$\displaystyle \forall$ x, y, z : f (f (x, y), z) = f (x, f (y, z))
	$\displaystyle \wedge$	$\displaystyle \forall$ x : g(b, x) = x $\displaystyle \wedge$ g(x, b) = x
	$\displaystyle \wedge$	$\displaystyle \forall$ x, y, z : g(g(x, y), z) = g(x, g(y, z))
	$\displaystyle \wedge$	$\displaystyle \forall$ x, y, z : g(f (x, y), z) = f (g(x, z), g(y, z))
	$\displaystyle \wedge$	$\displaystyle \forall$ x, y, z : g(x, f (y, z)) = f (g(x, y), g(x, z))