Quantifier Elimination for the Reals with a Predicate for the Powers of Two
journal contributionposted on 01.01.2005, 00:00 by Jeremy AvigadJeremy Avigad, Yimu Yin
In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretical argument, which provides no apparent bounds on the complexity of a decision procedure. We provide a syntactical argument that yields a procedure that is primitive recursive, although not elementary.