I have a problem to show that the following definition is sound.
Definition: Let $\Theta_1$ and $\Theta_2$ be order types. We say $\Theta_1 \prec \Theta_2$ If there are order sets $\langle A_1,\prec_1\rangle $ and $\langle A_2,\prec_2\rangle$ of order type $\Theta_1$ and $\Theta_2$ respectively such that $A_1$ is similar to a subset of $A_2$.
Prove that the definition is sound.
What is "sound" in this context means? And How can I prove it?
Thank you