Timeline for Non standard extension of real numbers via nonprincipal ultra filters
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2017 at 12:29 | vote | accept | Ali Taghavi | ||
| Apr 20, 2017 at 12:49 | answer | added | Mikhail Katz | timeline score: 5 | |
| Apr 19, 2017 at 13:38 | comment | added | Mikhail Katz | math.stackexchange.com/a/280935/72694 is a related answer by @AndreasBlass. | |
| Apr 19, 2017 at 12:02 | comment | added | Mikhail Katz | Some articles related to this can be found in this MSE post. There are $2^c$ ultrafilters but also $2^c$ non-isomorphic fields when $\neg CH$, so straightforward "counting" does not seem to allow one to decide. | |
| Apr 12, 2017 at 18:11 | comment | added | Paul McKenney | Just to finish the proof, there are always nonequivalent nonprincipal ultrafilters (since there are $2^{2^{\aleph_0}}$-many nonprincipal ultrafilters on $\mathbb{N}$ and only $2^{\aleph_0}$-many bijections from $\mathbb{N}$ to itself), so under CH the answer is no. But I think the answer is probably no just in ZFC. | |
| Apr 11, 2017 at 11:03 | comment | added | Michael Greinecker | A question that addresses the result mentioned by YCor can be found here. | |
| Apr 11, 2017 at 9:34 | history | edited | YCor |
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| Apr 11, 2017 at 9:34 | comment | added | YCor | I think it's known that under CH, all ultrapowers $\mathbb{R}_U$ are isomorphic. Maybe somebody more familiar known more about this. | |
| Apr 11, 2017 at 9:15 | history | asked | Ali Taghavi | CC BY-SA 3.0 |