Timeline for Are these theories of real and complex number biinterpretable?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2022 at 1:25 | comment | added | Joe Shipman | @AlexKruckman , you don’t need odd degree, you only need odd prime degree, as I proved in 2007. — Joe Shipman | |
| Sep 16, 2021 at 8:07 | history | edited | Oscar Cunningham | CC BY-SA 4.0 |
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| Sep 13, 2021 at 17:23 | vote | accept | Oscar Cunningham | ||
| Sep 13, 2021 at 16:59 | comment | added | Emil Jeřábek | Ok, done. ----- | |
| Sep 13, 2021 at 16:55 | answer | added | Emil Jeřábek | timeline score: 10 | |
| Sep 8, 2021 at 20:08 | comment | added | Oscar Cunningham | @EmilJeřábek Thanks. It looks like your comment has the community support. If you add it as an answer I'll accept it. | |
| Sep 8, 2021 at 20:07 | comment | added | Oscar Cunningham | @AlexKruckman Thanks, I've fixed it. | |
| Sep 8, 2021 at 11:22 | history | edited | Oscar Cunningham | CC BY-SA 4.0 |
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| Sep 8, 2021 at 5:32 | comment | added | Emil Jeřábek | While we are talking axiomatizations, $\mathrm{Th}(\mathbb C,0,1,+,\cdot,\bar{})$ is axiomatized by algebraically closed fields + $\bar z$ is an automorphism of order $2$. | |
| Sep 7, 2021 at 20:28 | comment | added | Alex Kruckman | To axiomatize RCF, in addition to saying that $-1$ is not a sum of squares and every odd-degree polynomial has a root, you need to say that for all $a$, $a$ or $-a$ is a square. | |
| Sep 7, 2021 at 19:04 | comment | added | Asaf Karagila♦ | @Emil: Imagine how much money we can make if we start charging a fee for constants. We can fund whole research centres with minimal bureaucracy! | |
| Sep 7, 2021 at 16:25 | comment | added | Emil Jeřábek | $\mathrm{Th}(\mathbb R,0,1,+,\cdot)$ is bi-interpretable with $\mathrm{Th}(\mathbb C,0,1,i,+,\cdot,\bar{})$ (you don’t really need $0$ and $1$ in either structure, they are definable). As you say, bi-interpretations preserve the automorphism group, so the result is not true without the $i$ constant. The thing is, model theorists are generally used to take constants from the model for free. | |
| Sep 7, 2021 at 16:08 | history | edited | Oscar Cunningham | CC BY-SA 4.0 |
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| Sep 7, 2021 at 15:54 | history | asked | Oscar Cunningham | CC BY-SA 4.0 |