Timeline for What theories are larger than the real closed field but still decidable?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 5, 2023 at 1:13 | vote | accept | Sidharth Ghoshal | ||
| Jan 11, 2023 at 4:28 | answer | added | user44143 | timeline score: 8 | |
| Jan 11, 2023 at 2:38 | history | became hot network question | |||
| Jan 10, 2023 at 22:54 | answer | added | Ali Enayat | timeline score: 12 | |
| Jan 10, 2023 at 19:05 | comment | added | Sidharth Ghoshal | Well “thing” also has a semantic meaning so we might invent some new sentence but actually that sentence is equivalent to something in the original real closed field. Ex: if “thing” was a new relation that was identical to the $<$ relation. But that case is obvious “thing” could seem like it’s new but really it’s not. I might even say we know “thing” is different BECAUSE the higher runtime of decidability tells us so. | |
| Jan 10, 2023 at 18:48 | comment | added | Noah Schweber | I think this is a good question, but I'm a bit confused by the phrasing: "AND we are able to prove new sentences which were not expressible before" seems a trivial condition. You're talking about theories of the form $Th(\mathbb{R};+,\times, [thing])$ for some new relation/function $[thing]$, right? In that case, you'll trivially be able to prove lots of newly-expressible things in this theory, since any theory of such a form is complete. | |
| Jan 10, 2023 at 18:43 | history | edited | Sidharth Ghoshal | CC BY-SA 4.0 |
added 4 characters in body
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| Jan 10, 2023 at 18:38 | history | asked | Sidharth Ghoshal | CC BY-SA 4.0 |