Timeline for Surreal numbers vs. non-standard analysis
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2019 at 23:35 | comment | added | Philip Ehrlich | @Mike. I am not aware of the existence of a "most natural (such) isomorphism". | |
| Apr 26, 2019 at 6:00 | comment | added | Mike Battaglia | Is there in any way a "most natural isomorphism" between the surreals and hyperreals? For instance, is there some "best" way to map $\omega$ to a hypernatural, and if so, do we know whether it is prime or composite, what $\sin(\omega)$ is, etc? | |
| Jul 29, 2018 at 14:29 | comment | added | Joel David Hamkins | OK, good, that is what I had thought. | |
| Jul 29, 2018 at 14:26 | comment | added | Philip Ehrlich | @Joel (Continued): Thus far, there has been little cross-fertilization between the surreals and NSA, and as such there is no reason at present why one would want to use No or various subfields of No as the universe of a nonstandard model of analysis. It would simply require extra work with little gain. However, I would not rule out cross-fertilization down the line, which would make the marriage of the two systems desirable. | |
| Jul 29, 2018 at 14:26 | comment | added | Philip Ehrlich | @Joel. Yes, Joel. While No does not come equipped with all the relational extensions one needs to do NSA, one can induce all such relational extensions by employing an isomorphism of ordered fields from No onto an On-saturated model of say Keisler’s axioms for hyperreal fields. In fact, since every real closed field is isomorphic to an initial subfield of No, one can do the same for any hyperreal field. | |
| Jul 29, 2018 at 13:41 | comment | added | Joel David Hamkins | Could you clarify whether the saturation property of the surreals includes a class resplendency property, by which we would get classes corresponding to the transfer of arbitrary functions and relations on the reals? (See also my comments below on the answer of Katz.) | |
| Mar 22, 2012 at 8:08 | vote | accept | James Propp | ||
| Mar 19, 2012 at 19:06 | history | answered | Philip Ehrlich | CC BY-SA 3.0 |