The real field with convergent generalized power series

Source abstract

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [ 0 , 1 ] [0,1] by a series ∑ c n x α n \sum c_{n} x^{\alpha _{n}} with 0 ≤ α n → ∞ 0 \leq \alpha _{n} \rightarrow \infty and ∑ | c n | r α n > ∞ \sum |c_{n}| r^{\alpha _{n}} > \infty for some r > 1 r>1 is definable. This expansion is polynomially bounded.