# Tagged Questions

**13**

votes

**2**answers

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

I've read these words: "How many ultra products $ā_Uā$ 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

**2**answers

788 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 ...