Structures of Finite Punctual Dimension \(n>2\)

In this paper we prove the primitive recursive analogue of Goncharov’s finite computable dimension n theorem [12, 13]. In the case of structures with computable dimension \(n>2\) , a certain elementary trick suffices. However in the primitive recursive case, this elementary trick no longer sufficies. Our first theorem shows that a direct construction of structures of punctual dimension \(n>2\) is provably necessary. Our second theorem is a direct construction of these structures. This work extends the earlier result of Melnikov and Ng [18].