COMPUTABLE STRUCTURE THEORY ON ω1 USING ADMISSIBILITY
NOAM GREENBERG AND JULIA F. KNIGHT
Abstract We use the theory of recursion on admissible ordinals to develop an analogue of classical computable model theory and effective algebra for structures of size 1, which, under our assumptions, is equal to the continuum. We discuss both general concepts, such as computable categoricity, and particular classes of examples, such as fields and linear orderings.
§1. Introduction. Our aim is to develop computable structure theory for uncountable structures. In this paper we focus on structures of size 1. The fundamental decision to be made, when trying to ...