User blog comment:DontDrinkH20/H-Boogol-Boogol Bit by bit: PART 1: Model Theory 101/@comment-35470197-20180901140237

> 6 ... \(v_n\) is NOT a free variable in \(\varphi\)

Typo of \(\forall \v_n(\varphi)\). (There is a similar typo in 7.)

> Sadly, it turns out that Godel's incompleteness theorem shows that EVERY system of mathematics which doesn't imply a contradiction has an undecidable sentence.

Common mistake. See here.

> 1 ... then \(t_0^{\mathcal{L}}(x_0 \ldots x_n)\)

Typo of \(t_0^{\mathcal{M}}\). (There are similar typos around it.)