How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
in [Logic]
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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
From: Aatu Koskensilta on 3 Jul 2010 08:48 Charlie-Boo <shymathguy(a)gmail.com> writes: > On Jun 29, 9:13�am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> Charlie-Boo <shymath...(a)gmail.com> writes: >> > ZFC was designed to avoid paradoxes by making explicit what can be a >> > set. �It doesn't do anything else except what the Peano Axioms give >> > it. >> >> Does PA give us Borel determinacy? Is Borel determinacy trivial? > > Prove ZFC can prove it and PA can't. The details are explained in Ross Bryant's Master's Thesis. You won't understand any of it, alas. -- 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 14:05
Charlie-Boo <shymathguy(a)gmail.com> writes: > And you won't post it, alas, so people could quickly and easily see it > and debunk it like the other BS references. You want me to post Ross Bryant's Master's Thesis? You'll find it online at: http://www.cas.unt.edu/~rdb0003/thesis/thesis.pdf -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |