13
votes
2answers
386 views

Why does CH imply that there is a unique ultrapower of $\mathbb{N}$?

I've read these words: "How many ultra products $āˆ_Uā„•$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ā„•$? If continuum hypothesis(CH) holds, then obviously just one ..." i ...
4
votes
2answers
798 views

Are all countable, nonstandard models of arithmetic given by ultrapowers?

Countable models of PA fall into two categories: the standard one $(\omega, S)$ and the nonstandard ones (all the rest). The only way I've seen to construct a nonstandard model is through taking an ...