Timeline for Undefinability of $\mathbb{Z}$ in the reals
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 24, 2017 at 12:29 | comment | added | Gerald Edgar | Said another way: "ring generated by" is a second-order concept. It cannot be stated in the first-order language of $(\mathbb{R}, +, -, < , 0, 1)$. | |
| Apr 24, 2017 at 11:56 | comment | added | Mohammad Golshani | It is not definable in that structure. Note that by definability, I mean first order definable in the structure | |
| Apr 24, 2017 at 11:56 | comment | added | Duchamp Gérard H. E. | I am not a specialist, but "naively", if you have a "real closed field" $K$, cannot you define $\mathbb{Z}$ as the ring generated by $1_K$ ? | |
| Apr 24, 2017 at 11:53 | comment | added | Mohammad Golshani | Thanks, are there proofs avoiding Godel's incompleteness theorem too. When writing the question, I had the idea of some different proof (maybe not using Godel's theorem). | |
| Apr 24, 2017 at 11:34 | history | answered | Mikhail Katz | CC BY-SA 3.0 |