Timeline for Examples of first-order claims about the reals that are not preserved under forcing
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2023 at 13:59 | audit | First answers | |||
| Nov 2, 2023 at 14:25 | |||||
| Oct 26, 2023 at 7:13 | audit | First answers | |||
| Oct 26, 2023 at 7:17 | |||||
| Oct 25, 2023 at 2:32 | vote | accept | Andrew Bacon | ||
| Oct 24, 2023 at 17:10 | comment | added | Noah Schweber | @spaceisdarkgreen Oh yeah (FWIW somewhere on here there's an embarrassing comment by me getting this wrong, which is subsequently corrected by Alex Kruckman IIRC; it still stings, so the fact is fresh in my mind :P). | |
| Oct 24, 2023 at 17:08 | comment | added | spaceisdarkgreen | @NoahSchweber lol I was puzzling over how much second order arithmetic that theory could support without being able to clinch that it’s (simply in retrospect) all of it. | |
| Oct 24, 2023 at 17:04 | comment | added | Noah Schweber | @AndrewBacon Then things change dramatically. See my answer. | |
| Oct 24, 2023 at 16:06 | comment | added | Andrew Bacon | I didn't actually know this theory was decidable. What about expanding the signature, but keeping it first-order? If we add a predicate for the natural numbers, then the theory interprets arithmetic and so this sort of argument isn't available. | |
| Oct 24, 2023 at 15:40 | comment | added | spaceisdarkgreen | @GEdgar Correct, added a reference. | |
| Oct 24, 2023 at 15:39 | history | edited | spaceisdarkgreen | CC BY-SA 4.0 |
added 237 characters in body
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| Oct 24, 2023 at 15:31 | comment | added | GEdgar | Decidability here is due to Tarski, I believe. The key thing in the proof is "quantifier elimination". | |
| Oct 24, 2023 at 15:21 | history | answered | spaceisdarkgreen | CC BY-SA 4.0 |