Timeline for Are all free groups linear, i.e., admit a faithful representation to GL(n,K) for some field K ?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2015 at 2:14 | answer | added | owb | timeline score: 10 | |
| S Mar 20, 2013 at 19:30 | vote | accept | Dietrich Burde | ||
| Mar 20, 2013 at 8:35 | vote | accept | Dietrich Burde | ||
| S Mar 20, 2013 at 19:30 | |||||
| Mar 19, 2013 at 19:35 | comment | added | Benjamin Steinberg | Yes, but there are proofs of compactness of first order logic that don't explicitly go through ultraproducts such as the original one via Godel's completeness theorem. But it is true that the compactness of first order logic is equivalent to the existence of non-principal ultrafilters if I understand correctly. | |
| Mar 19, 2013 at 18:49 | comment | added | YCor | Aren't ultraproducts and compactness of first logic are pretty much the same with different points of view? | |
| Mar 19, 2013 at 18:08 | comment | added | Benjamin Steinberg | I believe that instead of using ultrafilters one can prove this by the compactness of first order logic by interpreting existence of a faithful representation as an infinite collection of first order statements in the theory of algebraically closed fields of characteristic 0 and then using compactness because any finite subset of these statements is satisfied by using the finitely generated case. Hopefully a model theorist will pipe in. | |
| Mar 19, 2013 at 16:07 | answer | added | YCor | timeline score: 26 | |
| Mar 19, 2013 at 15:29 | answer | added | Misha | timeline score: 25 | |
| Mar 19, 2013 at 14:15 | history | asked | Dietrich Burde | CC BY-SA 3.0 |