Timeline for Model theory of the complex numbers with conjugation
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2021 at 7:06 | comment | added | Joel David Hamkins | Yes, it is a (parametric) bi-interpretation of theories. | |
| Sep 7, 2021 at 15:56 | comment | added | Oscar Cunningham | @JoelDavidHamkins When you mention bi-interpretation above, do you mean that it's a biinterpretation of the theories, or merely of the models? I've asked a question about this here. | |
| Nov 8, 2019 at 11:00 | vote | accept | user221330 | ||
| Nov 6, 2019 at 23:25 | comment | added | Joel David Hamkins | Ah, you are right. I have edited. | |
| Nov 6, 2019 at 23:09 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 557 characters in body
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| Nov 6, 2019 at 22:40 | comment | added | Alex Kruckman | There's a little bit of a hitch with QE, because the theory of $\langle\mathbb{R},+,\cdot,0,1\rangle$ does not have QE! You have to throw in the ordering $\leq$. So for example the formula $\exists x\, (x = \overline{x}\land x^2 = y)$ which defines the non-negative real numbers in $\mathbb{C}$ is not equivalent to a quantifier-free formula. On the other hand, model-completeness transfers from $\mathbb{R}$ to $\mathbb{C}$ with conjugation for exactly the reason you give: the interpretation involves only quantifier-free formulas. | |
| Nov 6, 2019 at 21:19 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 289 characters in body
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| Nov 6, 2019 at 21:10 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |