Speaker: Hakim Walker, GWU
Title: Computable isomorphisms between (2,1):1 structures

Abstract: A (2,1):1 structure consists of a countable set A (usually the natural numbers) and a function f that maps, to each element of A, either exactly one element of A or exactly two elements of A. Similar structures have been studied recently by Harizanov, Cenzer, Remmel, and Marshall, particularly the complexity of isomorphisms between such structures. In this talk, we will begin by presenting some of the basic properties of these structures, particularly the types of orbits under f, which can be interpreted as directed graphs. Then we will discuss some computability-theoretic results, including two classes of (2,1):1 structures that are computably categorical, i.e., every two computable copies of the structure have a computable isomorphism between them. Finally, we will conclude with an application to the Collatz conjecture.