Adele Padgett (McMaster University)

Regular solutions of systems of transexponential-polynomial equations

It is unknown whether there are o-minimal fields that are transexponential, i.e., that define functions which eventually grow faster than any tower of exponential functions. In past work, I constructed a Hardy field closed under a transexponential function $E$ which satisfies $E(x+1) = \exp E(x)$. Since the germs at infinity of unary functions definable in an o-minimal structure form a Hardy field, this can be seen as evidence that the real field expanded by $E$ could be o-minimal. To prove o-minimality, a better understanding of definable functions in several variable is likely needed. I will discuss one approach using a criterion for o-minimality due to Lion. This ongoing work is joint with Vincent Bagayoko and Elliot Kaplan.