Title: The tree of tuples of a structure
by Matthew Harrison-Trainor (Victoria University of Wellington, New Zealand) as part of Computability theory and applications
Given a countable structure, one can associate a tree of finite tuples from that structure, with each tuple labeled by its atomic type. This tree encodes the back-and-forth information of the structure, and hence determines the isomorphism type, but it is still missing something: with Montalban I proved that there are structures which cannot be computably (or even hyperarithmetically) recovered from their tree of tuples. I’ll explain the meaning of this result by exploring two separate threads in computable structure theory: universality and coding.