I am reading Charles Pinter's "Set Theory" and I found an exercise which I can't resolve. Maybe someone can help me. It says:
We will consider pairs $(B,G)$ where $B \subseteq A$, and $G$ is an order relation in $B$ which well-orders $B$. Let $A^*$ be the family of all such pairs $(B,G)$. We introduce the symbol $<$ and define $(B,G) < (B',G')$ if and only if:
a) $B \subset B'$
b) $G \subset G'$
c) $x \in B, y \in B' \setminus B \implies (x,y) \in G'$.
Verify that $<$ is a partial order relation in $A^*$.
Thanks for your help