How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: Jesse F. Hughes on 1 Jul 2010 14:31 Charlie-Boo <shymathguy(a)gmail.com> writes: > Yes, and as a Conservative you know the creed that to name a book is > to defeat your enemy - especially if it is very hard to obtain. (And > to make sure, refuse to quote from it!) You live in Cambridge, MA. You can't throw a rock without hitting a nearby university library. How hard is it to get the book that Moe mentioned? Heck, ask one of your MIT grad student party buddies to get it for you. -- "The math doesn't care about their mortgages. It doesn't care about their political needs. [...] Today's mathematicians have to hate mathematics because mathematics doesn't look out for them. It doesn't pay attention to their needs." --- JSH analyzes mathematicians
From: Aatu Koskensilta on 2 Jul 2010 09:33 herbzet <herbzet(a)gmail.com> writes: > herbzet wrote: > >> For classical logic the following sets are extensionally equivalent: > > Well, that's not exactly right, but you know what I'm getting at. Such imprecision! And on sci.logic! You should be deeply ashamed of yourself. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: herbzet on 3 Jul 2010 01:56 Aatu Koskensilta wrote: > herbzet writes: > > herbzet wrote: > > > >> For classical logic the following sets are extensionally equivalent: > > > > Well, that's not exactly right, but you know what I'm getting at. > > Such imprecision! And on sci.logic! You should be deeply ashamed of > yourself. I wuz tired.
From: Aatu Koskensilta on 3 Jul 2010 08:40 Charlie-Boo <shymathguy(a)gmail.com> writes: > How do you know that all of the logical argument can be formalized in > ZFC? The logic pixie told me so. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 3 Jul 2010 08:44
Charlie-Boo <shymathguy(a)gmail.com> writes: > On Jun 29, 10:16�am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > >> It's in Shelah's _Cardinal Arithmetic_ p.3245 - >> 4325238532. Basically, you just do a triple-fold transfinite >> recursion over a coherent extender sequence to obtain a suitable >> premouse, and iterate the upward Mostowski collapsing lemma a few >> times. To remove the extendible cardinal introduce some Aronszjan >> trees using Sacks forcing. > > Where's the part about how ZFC is used to do it? Pages 3219845327852387532 - 4321412421. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |