Closed marethyu closed 6 months ago
I see this is fixed, but I'm not convinced this was ever actually a typo: the family of structures that interpret $c$ as $1/K$ for $K \geq 1$ do satisfy all of $\Gamma$, not just some finite $\Gamma_0 \subseteq \Gamma$, and hence satisfy $\Gamma_0$ by monotonicity (realising this is part of the exercise of "prove this in detail"). But perhaps presenting it in the updated way makes it easier to understand…
Yes, it was not actually a typo, but I also thought it would be easier to follow this way (as evidenced by @marethyu 's suggesting the change - thanks BTW Jimmy!)
If I'm not mistaken, $\mathcal{Q}'\models\Gamma\cup\Delta_0$ should be $\mathcal{Q}'\models\Gamma_0\cup\Delta_0$ for some finite $\Gamma_0\subseteq\Gamma$, since $\Gamma$ could be infinite?
Also,
\{0<c\}
should be\{\Obj{0}<c\}
.