Timeline for The universe of sets, existential quantification in set theory
Current License: CC BY-SA 3.0
4 events
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| Mar 4, 2016 at 16:39 | comment | added | Andreas Blass | @PeterLeFanuLumsdaine Yes, I regard NBG as being "essentially" ZF. But I think that, if one regards proper classes as actually existing entities, then there is no reason to restrict the comprehension axiom to formulas without class quantifiers, and so MK is a more reasonable theory to use than NBG. In other words, I think of MK as the natural theory of sets and classes, whereas NBG is a technical variant of ZFC with some advantages over ZFC (like finite axiomatizability) and some disadvantages (like failure of induction in general). | |
| Mar 4, 2016 at 16:35 | comment | added | Peter LeFanu Lumsdaine | One extra point to an excellent answer: von-Neumann–Bernays–Gödel set theory gives a setting much closer to ZFC than Morse–Kelly (precisely, NBG is conservative over ZFC) where one can talk directly about proper classes and so literally make a statement “the class of all sets is proper”. | |
| S Mar 4, 2016 at 16:32 | history | answered | Andreas Blass | CC BY-SA 3.0 | |
| S Mar 4, 2016 at 16:32 | history | made wiki | Post Made Community Wiki by Andreas Blass |