Timeline for Is Quine's Mathematical Logic "ML" consistent with Azcel's Extensionality?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 9 at 16:17 | comment | added | Zuhair Al-Johar | @EmilJeřábek , ML is Quine's Mathematical Logic. ML to NF is like MK to ZF with the difference that quantifiers must be bounded by the universe of sets in stratified comprehension of ML. See google.iq/books/edition/Mathematical_Logic_Revised_Edition/…, see also, books.google.iq/… | |
| Sep 9 at 10:46 | comment | added | Zuhair Al-Johar | @JamesEHanson, transitive closures are defined using the class machinery of ML and doesn't depend on the NF part of ML. ML (like MK) proves the existence of a transitive closure for every set. The class comprehension axiom schema of ML is not stratified! | |
| Sep 9 at 6:59 | comment | added | Emil Jeřábek | What is ML, and how it relates to NF? | |
| Sep 9 at 2:58 | comment | added | James E Hanson | Actually now that I think about it that argument doesn't even establish the existence of transitive closures because the definition of transitivity isn't stratified. | |
| Sep 9 at 0:04 | comment | added | James E Hanson | In any case, a place to look would be Thomas Forster's book Set Theory with a Universal Set, which has some discussion of strong extensionality axioms in $\mathsf{NF}$. | |
| Sep 9 at 0:01 | comment | added | James E Hanson | This might be sensitive to how you define transitive closure. In $\mathsf{NF}$, for instance, there's going to be a least transitive set containing any given set $X$ (obtained by taking the intersection of all transitive sets $Y \supseteq X$), but there might be definable transitive subclasses of this set containing $X$. In principle one might define the strong extensionality axiom using a more restrictive definition of transitive closure that isn't actually a set. | |
| Sep 8 at 21:41 | comment | added | Zuhair Al-Johar | @PeterLeFanuLumsdaine, yes! | |
| Sep 8 at 21:04 | comment | added | Peter LeFanu Lumsdaine | To be clear: you intend the axiom Aczel calls “$AFA_2$” in his book, stating that every graph has at most one decoration? | |
| Sep 8 at 20:51 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |