The iota ($\iota$) and script A ($\mathcal{A}$) are determiners, not quantifiers in the usual sense; they’re described later, in the slides titled **Definite Determiners** and **Indefinite Determiners**. The expression $\iota x.F(x)$ is a term representing the unique entity $x$ such that $F(x)$ is true when such an entity exists and is undefined otherwise; see also this web page. $\mathcal{A}$ is the indefinite counterpart of $\iota$: $\mathcal{A}x.F(x)$ selects any entity $x$ such that $F(x)$ is true. Thus, $\iota$ functions somewhat like the definite article _the_ , while $\mathscr{A}$ functions rather like the indefinite article _a(n)_. The examples in the relevant slides are fairly clear.