The study of punctual structures considers what happens to the computation of structures and their isomorphisms when we forbid the use of unbounded search, that is, the restriction to primitive recursion.
We will introduce punctual presentations and consider primitive recursive isomorphisms. Since the inverse of a primitive recursive function is not necessarily primitive recursive, we obtain a reduction between punctual structure. Therefore we consider the punctual degrees for each fixed structure as the collection of punctual presentations under primitive recursive isomorphism. This means that we have a new degree structure to investigate for each punctual structure! We will discuss the current knowledge of the structural aspects of punctual degrees including density and lattice embeddings, as well as punctual dimension in relation to the punctual degrees.