A Reformulation of Z-Reg.2
in [Logic]
|
From: zuhair on 17 Jun 2010 23:46 On Jun 17, 3:39 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Jun 17, 2:49 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > On Jun 17, 12:02 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Jun 16, 7:03 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > > I haven't looked over your new formulations, but last night I did > > > > > figure out a way to formulate your compression schema so that it and > > > > > your union axiom entail the separation(with built in extensionality) > > > > > schema, while the separation schema (with built in extensionality) > > > > > entails your compression schema. > > > > > How can you do that without pairing and power??? I don't see a way to > > > > do that. > > > > Actually it would be rather interesting to see your proof that unique > > > > separation with union only can prove my comprehension schema, > > > > Then my formulation must not be equivalent with yours. > > > > So you're not claiming that your unique comprehension entails your > > > unique separation (ordinary separtion but with uniqueness quantifier)? > > > If you're not claiming that, then that would make better sense to me > > > from what I though you had previously claimed. > > > Moe I think you are confused. > > (1) Ah, I missed your word 'only' in "your proof that unique > separation with union only can prove my comprehension schema" > > I did not say ONLY. > > What I said is that unique separation (that is exactly: separation > schema except uniqueness quantifier) proves MY reversion (which I > haven't posted) of your unique comprehension. And it's trivial, since > MY re-version is just an instance of unique separation. > > (2) Sorry, I meant the other direction: Do you claim unique separation > (exactly: separation schema except uniqueness quantifier) with union > entails unique comprehension? > > But you answered that below, and it's fine, since your answer is 'no'. > > > However what I am NOT claiming is that my comprehension schema > > follows from unique separation alone without pairing , union and > > power. > > Ah, okay. > > (If I recall, you were saying something to the effect in a previous(?) > thread that the two axiomatizations were equivalent? But you're not > saying that now, okay.) > > Anyway, I've not looked at your new formulations or posted my > suggested simplification of your earlier version , so I can't judge at > this time whether your proof of unique separation from unique > comprehension and union is okay or not. I only know that I was able to > make it work by revising one or your earlier versions of unique > comprehension. I'll try to check your latest version this week or next > week. > > MoeBlee By the way there are no multiple versions of unique comprehension, all of them are the same version exactly but written in different ways. So theory A in this post is exactly the same one present int he earlier post. Zuhair
From: zuhair on 18 Jun 2010 17:36
On Jun 17, 3:39 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > On Jun 17, 2:49 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > On Jun 17, 12:02 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Jun 16, 7:03 pm, zuhair <zaljo...(a)gmail.com> wrote: > > > > > > I haven't looked over your new formulations, but last night I did > > > > > figure out a way to formulate your compression schema so that it and > > > > > your union axiom entail the separation(with built in extensionality) > > > > > schema, while the separation schema (with built in extensionality) > > > > > entails your compression schema. > > > > > How can you do that without pairing and power??? I don't see a way to > > > > do that. > > > > Actually it would be rather interesting to see your proof that unique > > > > separation with union only can prove my comprehension schema, > > > > Then my formulation must not be equivalent with yours. > > > > So you're not claiming that your unique comprehension entails your > > > unique separation (ordinary separtion but with uniqueness quantifier)? > > > If you're not claiming that, then that would make better sense to me > > > from what I though you had previously claimed. > > > Moe I think you are confused. > > (1) Ah, I missed your word 'only' in "your proof that unique > separation with union only can prove my comprehension schema" > > I did not say ONLY. > > What I said is that unique separation (that is exactly: separation > schema except uniqueness quantifier) proves MY reversion (which I > haven't posted) of your unique comprehension. And it's trivial, since > MY re-version is just an instance of unique separation. > > (2) Sorry, I meant the other direction: Do you claim unique separation > (exactly: separation schema except uniqueness quantifier) with union > entails unique comprehension? > > But you answered that below, and it's fine, since your answer is 'no'. > > > However what I am NOT claiming is that my comprehension schema > > follows from unique separation alone without pairing , union and > > power. > > Ah, okay. > > (If I recall, you were saying something to the effect in a previous(?) > thread that the two axiomatizations were equivalent? But you're not > saying that now, okay.) > > Anyway, I've not looked at your new formulations or posted my > suggested simplification of your earlier version , so I can't judge at > this time whether your proof of unique separation from unique > comprehension and union is okay or not. I only know that I was able to > make it work by revising one or your earlier versions of unique > comprehension. I'll try to check your latest version this week or next > week. > > MoeBlee Dear Moe Blee: Since matters might appear crumbled here, I presented the same theory exactly again, but written in a clearer manner in a separate post under the title: A=Z-Regularity. to go their click the following link: http://groups.google.com.jm/group/sci.logic/browse_thread/thread/190ff5c726528c2c?hl=en Zuhair |