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We study sets and groups definable in tame expansions of o-minimal structures. Let M = ⟨M, P ⟩ be an expansion of an o-minimal L-structure M by a dense set P. We impose three tameness conditions on M and prove a cone decomposition theorem for definable sets and functions in the realm of the o-minimal semi-bounded structures. The proof involves induction on(More)
The theory of (R, <, +, Z, Za) is decidable if a is quadratic. If a is the golden ratio, (R, <, +, Z, Za) defines multiplication by a. The results are established by using the Ostrowski numeration system based on the continued fraction expansion of a to define the above structures in monadic second order logic of one successor. The converse that (R, <, +,(More)