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Friday, January 29, 2016

**Abstract:** A Hardy Field is a subfield of the Ring of germs of real functions at infinity. That is closed under differentiation. Easy examples include the reals $\mathbb{R}$, the field of rational functions at infinity $\mathbb{R}(x)$ and the field of Laurent series at infinity $\mathbb{R}((x^{-1}))$. We will mention some properties about them, and their connection to truncation closed fields of transseries. If time permits we will mention some closure properties of truncation closed subsets of transseries.