Logic Seminar

Computable Isomorphisms between Partial Computable Injection Structures
Fri, 19 September, 2014 6:30pm

Speaker: Leah Marshall, GWU (graduate student)

Abstract: A partial computable injection structure is a mathematical structure consisting of a computable set of natural numbers and a partial computable, injective (1-1) function. The "shape" of these structures is determined by the orbits of the elements; that is, what happens when we apply our function to an element repeatedly. These structures can therefore be completely classified up to isomorphism by the numbers, types, and sizes of their orbits. However, we know that isomorphisms alone do not necessarily preserve the computability-theoretic properties of mathematical structures. We examine partial computable injection structures with computable isomorphisms, and we explain what goes wrong in structures without such computable isomorphisms. Additionally, we do the same for partial computable injection structures under Δ2-isomorphisms and Δ3-isomorphisms.


Share This Event