Timeline for Set theory in practice
Current License: CC BY-SA 2.5
10 events
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| Jul 31, 2010 at 6:19 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Mar 21, 2010 at 5:18 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Mar 21, 2010 at 0:19 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Mar 19, 2010 at 16:02 | comment | added | François G. Dorais | @Hans: It is common (but not necessary) to add structure to the set of atoms by adding new predicates and functions to the language. For example, you can make the atoms isomorphic to $\mathbb{R}$ by adding functions to add and multiply atoms together. | |
| Mar 19, 2010 at 8:43 | comment | added | Harry Gindi | The name urelement comes from the german-derived prefix ur- (primitive). Then urelement means "primitive element". | |
| Mar 19, 2010 at 7:45 | comment | added | abcdxyz | haha, the name urelement can be interpreted as a pun. urelement = your element. I don't know whether it was in the original intention or not, was Quine the one who gave that name? | |
| Mar 19, 2010 at 7:10 | comment | added | Hans-Peter Stricker | I always understood urelements as atoms or monads: totally propertyless entities, only distinguishable one from each other but not on behalf of their - not existent - properties. Such urelements alone give set theory another flavor. But it might be hard to see men - as opposed to women? - as such urelements. One might argue: something, that has properties, must have something like an inner structure, thus must be based on some kind of set. | |
| Mar 18, 2010 at 23:38 | comment | added | The Mathemagician | It seems to me,Pete-see my response above in addition-that unless you want to take a purely instrumentalist approach to mathematics,these issues need to be front and center for all of us.That's just my feeling on it. | |
| Mar 18, 2010 at 22:28 | comment | added | François G. Dorais | Excellent answer Pete! I wish more mainstream mathematicians were so well acquainted with foundational issues. Note that ZFA (ZF with Atoms, aka ZFU) is more popular than NFU. I don't know why wikipedia doesn't mention this theory. The main reason for NFU's "popularity" is that it has been shown consistent (relative to PA!) whereas the consistency of NF is still a wide open problem. With respect to foundations, I think this is by far one of the most unexpected results ever! | |
| Mar 18, 2010 at 22:07 | history | answered | Pete L. Clark | CC BY-SA 2.5 |