Punctual Presentability in Certain Classes of Algebraic Structures

Punctual structure theory is a rapidly emerging subfield of computable structure theory which aims at understanding the primitive recursive content of algebraic structures. A structure with domain N is punctual if its relations and functions are (uniformly) primitive recursive. One of the fundamental problems of this area is to understand which computable members of a given class of structures admit a punctual presentation. We investigate such a problem for a number of familiar classes of algebraic structures, paying special attention to the case of trees, presented both in a relational and functional signature.