All Questions

The standard proof of Tennenbaums's theorem uses the existence of recursively enumerable inseparable sets and is presented e.g. in Kaye [1, 2], Smith [3]. In the following, $\mathcal{M}$ will always ...

Let $\ulcorner \cdot \urcorner$ be a fixed encoding of formulas by numbers, e.g. let $\ulcorner \varphi \urcorner$ denote the Godel number of $\varphi$. Let $T$ be a first-order arithmetic theory, e....

Is there a first order statement about the natural numbers (not nonstandard analysis) such that the truth of the statement is easier to see in a nonstandard model? In other words, do nonstandard ...

I am attempting to write an expository paper on non-standard models of PA that is accesible to students taking an introductory graduate course in mathematical logic (covering Godel's incompleteness ...