Timeline for Union of a object (a set) in the Elementary Theory of the Category of Sets
Current License: CC BY-SA 3.0
7 events
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| Nov 21, 2011 at 18:37 | history | edited | Todd Trimble | CC BY-SA 3.0 |
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| Nov 21, 2011 at 15:26 | comment | added | Todd Trimble | One such "new foundations" is currently being developed by Voevodsky and others who are working at the interface between $\infty$-category theory and intensional type theory, under the rubric "homotopy type theory". But generally, we've moved past the point where we actively need to shoehorn mathematical concepts (like homotopy type) into a specifically set-theoretic framework, and doing so often introduces irrelevancies and complications. Let's just say it's nice, for purposes of relative consistency, that this can be done. (Cf. Conway's call for a "Mathematicians' Liberation Movement"!) | |
| Nov 21, 2011 at 14:42 | history | edited | Todd Trimble | CC BY-SA 3.0 |
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| Nov 21, 2011 at 12:33 | comment | added | Buschi Sergio | Not only, but set theory provides essential technical elements for the various demonstrations in various fields (transfinite induction, ordinal regular irraggiongibili, universes, etc. .. Vopenka). Then I think that today mathematic need a new foundation. | |
| Nov 21, 2011 at 12:30 | comment | added | Buschi Sergio | thank you very much for your reply Mr. Trimble. I just know a little of categorical logic, and internal logic of a topos, but I have to improve a lot of this large deep aspect of mathematic. I see that after Godel theorems we know that mathematics cannot have a foundation that ensure its consistency, and after category theory (and topos theory) we see the mathematic world no as a single "planet" but a system of different world, each totally different from the other, but "Set teory " keep its role of milestone of all mathematics, any structure, category is in last analysis a set (continue). | |
| Nov 21, 2011 at 8:56 | history | edited | Todd Trimble | CC BY-SA 3.0 |
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| Nov 21, 2011 at 8:50 | history | answered | Todd Trimble | CC BY-SA 3.0 |