Timeline for The existence of proper classes
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 31, 2012 at 17:19 | comment | added | Mike Shulman | Even if it is true that everything we prove using proper classes (and not referring explicitly to proper classes) could be proved without using them, that would have no bearing on the question of whether proper classes exist. | |
| Feb 11, 2012 at 8:16 | answer | added | Johan Wästlund | timeline score: 3 | |
| Feb 9, 2012 at 16:58 | comment | added | Andreas Blass | If I remember correctly, in the context of Ackermann's set theory one does need the proper classes; without them that theory is weaker than ZF. To fit this situation into my philosophical point of view, I'd say that what Ackermann's theory calls proper classes are really certain sets. That notion has some support in the Levy-Vaught interpretation of Ackermann set theory in a conservative extension of ZF, where both the sets and the classes of Ackermann are interpreted as certain sets in the sense of ZF. | |
| Feb 9, 2012 at 16:32 | comment | added | Pace Nielsen | If I read Andreas correctly, I think he was saying that in his philosophically motivated "model" of mathematics, there are no proper classes. That is not to say there are not other ways of thinking about mathematics, which are consistent, and make use of proper classes. | |
| Feb 9, 2012 at 15:42 | history | asked | Michael | CC BY-SA 3.0 |