Can someone help me how to prove that $\omega \_1$ is indefinite.

The thing is that I have always worked with proving that a certain term or $\in$-formula is definite, for which I was simply following the definition.

Here, the definitions are the following:

Let $ψ(v)$ be an $∈$-formula and let $t(v)$ be a term, both in the free variables $v$. 

Then

a) $ψ$ is definite iff for every transitive ZF− model $(M , ∈)$

$∀x ∈ M (ψ^M(x)↔ψ(x))$

b) $t$ is definite iff for every transitive ZF− model $(M ,∈)$

$∀x ∈ M$ $t^M(x) ∈ M$ and $∀x ∈ M $ $t^M(x ) = t(x )$