Abstract
In this paper we investigate the logical decidability and undecidability properties of relativity theories. If we include into our theory the whole theory of the reals, then relativity theory still can be decidable. However, if we actually assume the structure of the quantities in our models to be the reals, or at least to be Archimedean, then we get possible predictions in the language of relativity theory which are independent of ZF set theory.
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