Timeline for Union of a object (a set) in the Elementary Theory of the Category of Sets
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Nov 22, 2011 at 1:12 | comment | added | David Roberts♦ | I should add that my answer describes very roughly how to recover the concept of union for the material set theory extracted from a structural set theory. It doesn't describe 'union' in the structural set theory itself, where it is a meaningless construct. | |
| Nov 21, 2011 at 22:58 | comment | added | François G. Dorais | This is really a different topic, but the Union Axiom does not entail any typing violations, as Frege's Rule V did -- leading to Russell's Paradox, so it is really hard to compare the two. What do you mean that the Union Axiom is bad? | |
| Nov 21, 2011 at 22:55 | comment | added | François G. Dorais | David is talking about the interpretation of the Union Axiom in a topos. I'm doing the reverse: what does the Union Axiom say about the universe of sets seen as a topos. Well, it corresponds exactly to the existence of internal coproducts (modulo some elementary combinatorics). Note that these coproducts are significantly different from unions of subobjects, which is the literal translation of the union operation but lacks its full power. | |
| Nov 21, 2011 at 20:23 | comment | added | Buschi Sergio | thank you Dorais, and excuse me for the no too understable English. Of course the importance of the union is to allow the coproduct in Set. But the union is much more subdle (see the good reply of David Roberts above) it involve the trees of elements, is like a colimits of the inclusions of the union members in the maximal universe class. THis is the result of a bad generalization of the boolean operation on subsets (of a fixed set) to a general sets context, I seems is amost bad as the "axiom of class formation" that has led to Russel paradox. | |
| Nov 21, 2011 at 19:34 | history | answered | François G. Dorais | CC BY-SA 3.0 |