Leibniz Equivalence (slides)

Here are some slides for a talk on "Leibniz Equivalence" which includes some topics I've written some previous M-Phi posts about (Leibniz abstraction; the notion of abstract structure; possible worlds; the abstract/concrete distinction as modal).

The main things here are the accounts of:

(i) abstract structure: given a model $\mathcal{A}$, its abstract structure is a certain kind of second-order propositional function, ${\hat{\mathrm{\Phi }}}_{\mathcal{A}}$;
(ii) possible worlds: entities $w$ such that

$w={\hat{\mathrm{\Phi }}}_{\mathcal{A}}[\overrightarrow{R}]$

where $\overrightarrow{R}$ is a sequence of relations.