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Friday, November 20, 2020

**Abstract:** A metric structure $\mathfrak{M}$ is considered *approximately ultra-homogeneous* if for any finitely generated structure $A =\langle a_1,\dotsc,a_n\rangle$, embeddings $f,g:A \rightarrow \mathfrak{M}$, and $\varepsilon > 0$, there exists an automorphism $\phi$ on $\mathfrak{M}$ such that $d(\phi \circ f (a_i), g(a_i) ) < \varepsilon $. We show that there exists a separable approximately ultra-homogeneous Banach lattice $\mathfrak{BL}$ that is isometrically universal for separable Banach lattices by proving that finitely generated Banach lattices form a metric Fraïssé class. If time permits, we will also explore some interesting properties about $\mathfrak{BL}$.