Uniform bounds on growth in o-minimal structures

摘要

We prove that a function definable with parameters in an o-minimal structure is bounded away from Do as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in [1 1. Moreover, this remains true if the argument is taken to approach any element of the structure (or +oo), and the function has limit any element of the structure (or +co).