Timeline for How different category theories relate
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2011 at 11:00 | comment | added | Todd Trimble | @Mike: Well, true. I'm sometimes prone to understatement. :-) | |
| Jun 18, 2011 at 5:36 | comment | added | Mike Shulman | "not quite as strong" is quite an understatement! | |
| Jun 18, 2011 at 0:04 | comment | added | Todd Trimble | So-called "Mac Lane set theory" is not however the same as the set of assumptions formally adopted in the section on Foundations in Categories for the Working Mathematician. Mac Lane set theory is a membership-based set theory equal in strength to Lawvere's Elementary Theory of the Category of Sets (ETCS); it's not quite as strong as the assumption of ZFC + one inaccessible adopted in CWM. | |
| Jun 17, 2011 at 21:10 | comment | added | Mariano Suárez-Álvarez | @porton: your "Are you supposing me to read and understand all this?" is probably the worst you can say to someone who took the time to write such a helpful answer... | |
| Jun 17, 2011 at 20:48 | comment | added | Joel David Hamkins | Oh, if you don't find my answer helpful, then kindly please ignore it. Meanwhile, Mathias' work is quite interesting, although it is true that the systems he analyzes in the first article seem not to involve universes directly. The usual arguments I have seen giving the strength of the axiom of universes as inaccessible cardinals presupposes ZFC as a background theory, and if you weaken it to the theories Mathias attributes to Mac Lane, then I'm not sure how that comparison is affected. | |
| Jun 17, 2011 at 20:39 | comment | added | porton | You've given me some references, probably useful ones. But you haven't answered my question! (Or should I search for an answer through all your references?) | |
| Jun 17, 2011 at 20:35 | comment | added | porton | Are you supposing me to read and understand all this? I'm not a logician. But my quick search for the word "universe" in "The strength of Mac Lane set theory" reveals that that article does not even mention Grothendieck universes. How is this related with the logical system of "Categories for the Working Mathematician"? | |
| Jun 17, 2011 at 20:31 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 247 characters in body
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| Jun 17, 2011 at 20:24 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |