Saturday, April 2, 20162:30 pmNERDS: New England Recursion & Definability SeminarLocklin Hall, Room 232, Springfield College

# Computable categoricity, linear orders and permitting

## Marie Nicholson

### University of Connecticut

Remmel showed that a computable linear order *L* is computably categorical if and only if the order type of *L* has only a finite number of successivities. As part of the proof, Remmel assumes that *L* has infinitely many successivities and constructs another computable linear order *R*, which is not computably isomorphic to *L*, and a Δ^{0}_{2}-isomorphism *f* such that *f* is an isomorphism from *L* onto *R*. Hence showing that *L* is not computably categorical. In this talk I will discuss the conditions under which we can use permitting arguments to construct *f* below certain types of Δ^{0}_{2} degrees.