Timeline for Non-constructive existence proofs without AC?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2021 at 15:09 | comment | added | Hanul Jeon | What you described in your question is known as the existence property. It is known that Heyting arithmetic satisfies this property, and Hamkins' answer shows $\mathsf{ZF}$ does not satisfy it. Andrew Swan proved that $\mathsf{CZF}$ also does not satisfy the existence property, and if my memory serves right, $\mathsf{IZF}$ also does not have this property (maybe due to H. Friedman.) | |
| Mar 5, 2013 at 19:27 | history | edited | Rémi Peyre | CC BY-SA 3.0 |
typos
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| Mar 5, 2013 at 17:03 | comment | added | Joel David Hamkins | The term `constructive' is indeed over-loaded, but seems to be completely standard for these different usages. One has constructive logic, where excluded middle is not valid; constructive proofs, an informal concept meaning that the proof does not appeal to pure-existence axioms; and the constructible universe $L$, which is the model of set theory that Goedel had created to prove the relative consistency of ZFC+CH. | |
| Mar 5, 2013 at 14:42 | vote | accept | Rémi Peyre | ||
| Mar 5, 2013 at 13:46 | comment | added | Gerald Edgar | Maybe we heed help with terminology in headlines. Yesterday there was a question (mathoverflow.net/questions/123482 ) where "non-constructive" meant "proof uses the law of the excluded middle". | |
| Mar 5, 2013 at 12:51 | comment | added | Michael Greinecker | I once asked a related question: mathoverflow.net/questions/81082/… | |
| Mar 5, 2013 at 11:26 | answer | added | Joel David Hamkins | timeline score: 13 | |
| Mar 5, 2013 at 10:44 | history | asked | Rémi Peyre | CC BY-SA 3.0 |