Timeline for Representability of matroids over finite fields
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2018 at 15:44 | comment | added | Andreas Blass | Since linear representability of a given finite matroid over a field $F$ is a property of $F$ expressible in first-order logic, negative answers to Questions 2 and 3 follow from the compactness theorem of first-order logic. Then the completeness of the theory of algebraically closed fields of any fixed characteristic implies that a finite matroid representable over a field $F$ (and thus over its algebraic closure) is also representable over the algebraic closure of the prime field of the same characteristic. A negative answer to Q1 then follows. | |
| Oct 30, 2018 at 8:24 | vote | accept | Yuzhou Gu | ||
| Oct 30, 2018 at 7:17 | answer | added | Aaron Dall | timeline score: 8 | |
| Oct 30, 2018 at 4:34 | comment | added | LeechLattice | The answer to Q2 and Q3 is no, by considering possibilities of the characteristic set. | |
| Oct 30, 2018 at 3:56 | comment | added | Peter McNamara | I think the answer to all three questions is no, by a spreading out argument. | |
| Oct 30, 2018 at 1:18 | history | asked | Yuzhou Gu | CC BY-SA 4.0 |