Classes of structures with universe a subset of 1
Ekaterina Fokina, S.D. Friedman, Julia F. Knight, Russell Miller · Journal of Logic and Computation · 2013
We continue recent work on computable structure theory in the setting of ω1. We prove the analogue of a result from Fokina et al. (2012 J. Symbolic Logic, 77, 122–132) saying that isomorphism of computable structures lies ‘on top’ among Σ11 equivalence relations on ω. Our equivalence relations are on ω1. In the standard setting, Σ11 sets are characterized in terms of paths through trees. In the setting of ω1, we use a new characterization of Σ11 sets that involves clubs in ω1. Finally, we present some new results about ω1-computable categoricity for fields.