Timeline for What is lost in General Relativity without Hahn-Banach axiom in the ZF+HB set theory?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 9, 2023 at 17:03 | vote | accept | Bastam Tajik | ||
| Sep 9, 2023 at 15:31 | comment | added | Timothy Chow | @BastamTajik I think that before addressing that question, one must first grapple with the more fundamental question of how to develop basic analysis on the basis of ZF. See this MO answer for example. For example, there are annoying technicalities associated with developing measure theory purely on the basis of ZF. You might lose some theorems for some "technical" reasons that don't really have anything to do with Lorentzian geometry per se. | |
| Sep 9, 2023 at 12:50 | comment | added | plm | Hi Timothy, i think a more accurate statement would use "proved" rather than "derived", in particular "proved to exist" for solutions with desired properties -like cosmological solutions with desired curvature, stability of black holes, cosmic censorship,... Because to "derive" is what physicists do all the time, and it is mostly intuitive reasoning, often through formal manipulations carelessly generalizing from a few physical cases of interest, and almost always assuming any required mathematical hypothesis (like existence of solutions) or rather overlooking them. | |
| Sep 9, 2023 at 12:42 | comment | added | Bastam Tajik | Maybe I could ask what are the most general(least structure involved in) theorems lost in Lorentzian Geometry limiting one's self to ZF set theory. | |
| Sep 9, 2023 at 12:33 | history | answered | Timothy Chow | CC BY-SA 4.0 |