Uniform bounds on growth in o-minimal structures

Details Uniform bounds on growth in o-minimal structures Uniform bounds on growth in o-minimal structures

2007-03-27

arxiv.org/abs/math/0703776v4

Mathematics

Logic

3 pages. To appear in Mathematical Logic Quarterly

Scientific paper

10.1002/malq.200910031

We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity 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 a paper of Friedman and Miller. Moreover, this remains true if the argument is taken to approach any element of the structure (or plus/minus infinity), and the function has limit any element of the structure (or plus/minus infinity).

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