# Poster

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 Δ02-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 Δ02 degrees.