Timeline for Are the definable hyper-reals, using quantifiers only over the standard reals and natural numbers, the same as the algebraic numbers?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2017 at 12:30 | vote | accept | Joel David Hamkins | ||
| Feb 4, 2017 at 12:27 | comment | added | tomasz | @RamirodelaVega: I have not read your comment before. I see now that you're saying basically the same thing as I did in my answer. Sorry about that! | |
| Feb 4, 2017 at 12:24 | answer | added | tomasz | timeline score: 8 | |
| Feb 4, 2017 at 12:20 | comment | added | Joel David Hamkins | @tomasz Adding those predicates to the language is stronger than merely restricting the scope of all quantifiers to the standard reals, since in your language you can also quantify over the non-standard reals, if you want. As for which hyper-reals, take one that you like. I would be interested to know whether the answer depends on this. | |
| Feb 4, 2017 at 12:18 | comment | added | Joel David Hamkins | @RamirodelaVega I think you may be right! | |
| Feb 4, 2017 at 11:16 | comment | added | tomasz | So the language we are working in is $\{0,1,+,\cdot,\leq,{\bf N}^*,{\bf R}^{\textrm{st}}\}$, where ${\bf N}^*$ is a predicate for natural numbers and ${\bf R}^{\textrm{st}}$ is a predicate for standard reals? Which definition of hyperreals do you have in mind? | |
| Feb 4, 2017 at 6:44 | comment | added | Ramiro de la Vega | What if you add $\exists y(x=y)$ to your definition of $e$? Wouldn't the restricted-scope version work now? | |
| Feb 4, 2017 at 0:08 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 145 characters in body
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| Feb 3, 2017 at 23:55 | history | asked | Joel David Hamkins | CC BY-SA 3.0 |