Timeline for What are the advantages of the more abstract approaches to nonstandard analysis?
Current License: CC BY-SA 3.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Dec 17, 2015 at 18:22 | comment | added | Mikhail Katz | ... apparently handled more successfully in the more abstract approaches. Hopefully this can be clarified. | |
| Dec 17, 2015 at 18:22 | comment | added | Mikhail Katz | Cody, thanks for this. I am not sure this is really about axiomatics though. There is an axiomatic approach to Robinson's framework, developed by Hrbacek, Nelson, and others. Here you find infinitesimals within the real number system itself. But Robinson constructs an extension of $\mathbb{R}$ by compactness theorem and transfer principle is a consequence of the fact that it is an elementary extension, whereas for ultrapowers the transfer principle is a consequence of Los' theorem. So in this sense you end up with transfer in either case. The key seems to be in saturation that's... | |
| Dec 17, 2015 at 18:15 | history | edited | cody | CC BY-SA 3.0 |
NST -> NSA
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| Dec 17, 2015 at 18:11 | history | answered | cody | CC BY-SA 3.0 |