Timeline for Set theories that do require the existence of urelements?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2010 at 15:47 | comment | added | Mike Shulman | If you assume AC, then every set (even one containing atoms) can be well-ordered and is thus isomorphic to a von Neumann ordinal, which is a pure set (hereditarily contains no atoms). But in the absence of AC things can be more interesting, e.g. consider a permutation model of ZFA. | |
| Jan 25, 2010 at 14:01 | comment | added | Hans-Peter Stricker | Side note: If categorists tend to see sets as "bags of dots" (and categories as "bags of dots with arrows between them") why not measure category theory against a set theory which explicitely captures "bags of dots". Simply because the category of sets is equivalent to the category of sets with atoms (as I suppose)? | |
| Jan 25, 2010 at 13:50 | comment | added | Hans-Peter Stricker | Do you agree with my reading, then? | |
| Jan 25, 2010 at 13:42 | comment | added | Pete L. Clark | It's not your doing, but I parsed Axiom 11 incorrectly and got very confused. Better I think is: "There is no set which contains every atom." (I originally read the statement as "There is no set $S$ such that every element of $S$ is an atom", which made no sense at all.) | |
| Jan 25, 2010 at 13:34 | history | answered | Hans-Peter Stricker | CC BY-SA 2.5 |