# Computability theoretic properties of isomorphisms between partial computable injection structures

## Leah Marshall

### George Washington University

A partial computable injection structure consists of a computable set of natural numbers and a partial computable, injective (1-1) function. Clearly, the isomorphism type of such a structure is determined by the kinds and number of orbits of the elements under the function application. First, we investigate partial computable injection structures always having computable isomorphisms to other isomorphic structures, and we analyze what goes wrong in structures without such computable isomorphisms. Additionally, we do the same for partial computable injection structures under Δ_{2}-isomorphisms and Δ_{3}-isomorphisms.

Leah Marshall is a graduate student at George Washington University, working on a doctorate in computability theory under the supervision of Valentina Harizanov.