Timeline for A question regarding $ZFC^{-}$
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2014 at 2:41 | comment | added | François G. Dorais | In that case, the powerset axiom is really hard to beat! | |
| Dec 22, 2014 at 1:56 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
improved formatting
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| Dec 22, 2014 at 1:33 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
improved formatting
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| Dec 22, 2014 at 1:30 | comment | added | Thomas Benjamin | @FrançoisG.Dorais: Since there a great deal of such sets of axioms, the simplest and most 'economical' (i.e. the set with the fewest number of axioms) will do just fine, thank you. | |
| Dec 22, 2014 at 1:23 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
revised question in light of new information
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| Dec 13, 2014 at 14:04 | comment | added | François G. Dorais | Replacement is basically a special case of collection. Depending on how it is formulated, collection might give you a set that is larger than the range of your function, but you can always trim it down using comprehension. | |
| Dec 13, 2014 at 10:06 | comment | added | Thomas Benjamin | @FrançoisG.Dorais: Can you prove that Replacement is a consequence of $ZFC^{-}$? | |
| Dec 13, 2014 at 3:59 | answer | added | François G. Dorais | timeline score: 2 | |
| Dec 13, 2014 at 2:59 | comment | added | François G. Dorais | There are a great deal of such sets, so you probably need to be more specific. | |
| Dec 13, 2014 at 2:37 | comment | added | Thomas Benjamin | @FrançoisG.Dorais: Simply put, I am looking for some set of sentences in the language of set theory that will derive Powerset. Perhaps such a set does not exist, but it does not hurt to look. Perhaps some references of work done in this area will be a good start for me. | |
| Dec 13, 2014 at 2:18 | comment | added | François G. Dorais | Since powerset is a reasonably simple sentence, I can't really see what you're asking for. | |
| Dec 13, 2014 at 2:13 | comment | added | Thomas Benjamin | @FrançoisG.Dorais: Very well, then. So the question now becomes, what axioms $X$ (other than the trivial axiom Powerset) when added to $ZFC^{-}$, will derive Powerset as a theorem, and recover full ZFC? Thanks for the info, by the way. It is very much appreciated. | |
| Dec 13, 2014 at 2:08 | comment | added | François G. Dorais | I was using your definition. | |
| Dec 13, 2014 at 2:06 | comment | added | Thomas Benjamin | @FrançoisG.Dorais: ZFC- is ZFC-Powerset, correct? If so then this is different than $ZFC^{-}$. | |
| Dec 13, 2014 at 1:48 | comment | added | François G. Dorais | Replacement is a consequence of ZFC-. | |
| Dec 13, 2014 at 1:14 | history | asked | Thomas Benjamin | CC BY-SA 3.0 |