**Definition:** Let $C$ be a class of sets and $\mathcal{L}$ a first order relational language. We say $C$ is "outer definable" by $\mathcal{L}$ if there is a first order theory $T$ and for each $n_{R}$ - ary relational symbol $R\in \mathcal{L}$ there is a class $E_{R}\subseteq V^{n_{R}}$ such that: $\forall a\in V~~~(a\in C\Longleftrightarrow M_{a}\vDash T)$ which $M_a$ is a $\mathcal{L}$ - structure as follows: $Dom(M_a):=a~~,~~\forall R\in \mathcal{L}~~~~~R^{M_a}:=E_{R}\cap a^{n_R}$

**Question 1:** Is each class $C$ outer definable in the language of set theory?

If not then:

**Question 2:** Are $Ord$ and $Card$ outer definable in the language of set theory (or any other suitable relational language)?

**Question 3:** Is each class $C$ outer definable in some suitable first order relational language?