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Effective Mathematics of the Uncountable by Joel David Hamkins, Denis Hirschfeldt, Noam Greenberg

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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 image1, 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 ...

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