Abstract:
IfMis a o-minimal expansion of ordered eld of reals which contains a de nable function which can not dominated by polynomials, then exponential function appears as a de nable function. In this study rstly we introduce notions from model theory and o-minimality, then we see de nable functions in o-minimal structure forms a Hardy eld and we put valuation on Hardy eld. By the help of valuation we can show exponential function is de nable in a o-minimal expansion of ordered eld of reals which is not polynomially bounded.
