apologies in advance for the noob question. (Really rusty when it comes to order theory notation.)
Suppose I have a set $\Omega := \{\alpha,\beta_1,...,\beta_n\} $ (for some fixed $n\in\mathbb{N}$). I would like to succinctly express the following:
$\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad $ "$C$ is a subset of elements from $\Omega$ ordered in the following way:
$\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad$ 1. If $\alpha$ is in $C$, then it is placed first.
$\quad \quad \quad\quad\quad \quad\quad\quad\quad\quad\quad$ 2. All $\beta$'s in $C$ are placed in increasing order of their indeces."
I hope this is sufficiently precise; to help illustrate, here are a couple of examples of what I have in mind:
$\quad \bullet\ $ $C = (\omega, \beta_1,\beta_3)$
$\quad \bullet\ $ $C = (\beta_2,\beta_3)$
If there is no succinct, mathematical way to state this, then no worries! Thanks in any case.