# Monthly Archives: January 2020

## Non-standard Models of Arithmetic 14

MW: Recap: we showed that PAT implies ΦT, where ΦT is the set of all formulas

$\{\varphi\rightarrow\text{Con}(T_n+\varphi^\mathbb{N}):\varphi\in\text{L(PA)},n\in\omega\}$

Now we have to show the converse, that PA+ΦT  implies PAT. But first let’s wave our hands, hopefully shaking off some intuition, like a dog shaking off water.