An axiomatic construction is proposed for a model for the increase of infor
mation in an investigation. The model necessarily has a system of levels si
nd so is a graded algebra. Only four levels are possible with successively
3, 10, 137 and 10(38) elements. It is argued that these numbers indicate th
e appropriateness of the model in physics, but it is thought to have more g
eneral applicability.