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Uniform bounds on growth in o-minimal structures

Janak Ramakrishnan
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Abstract

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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Janak Ramakrishnan. 2007-03-27. Uniform bounds on growth in o-minimal structures. https://doi.org/10.1002/malq.200910031

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