How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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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
From: Alan Smaill on 3 Jul 2010 14:38 Charlie-Boo <shymathguy(a)gmail.com> writes: > On Jul 3, 2:28�pm, Charlie-Boo <shymath...(a)gmail.com> wrote: >> On Jul 3, 2:05�pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> >> > Charlie-Boo <shymath...(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 >> >> Thanks. �But where does he show proof lines with ZFC as their >> justification? �He refers to ZFC and makes claims regarding it, but >> all of his proofs and arguments are presented in normal mathematical >> terms with no reference to ZFC. >> >> 100 pages full of proofs and a handful of references to ZFC doesn't do >> it. > > And the proof that it can't be carried out in PA? CBL worked that out years ago. >> C-B > -- Alan Smaill
From: Jesse F. Hughes on 4 Jul 2010 08:59 Transfer Principle <lwalke3(a)lausd.net> writes: > If Aatu can say that PA is consistent, _period_, without any formal > proof whatsoever, then why can't Nguyen believe that PA is > inconsistent, _period_, without formal proof? Aatu said PA is consistent, _period_, without any formal proof? -- Jesse F. Hughes "If you believe there is any other truth but what is in your mind, you are deluding yourself." -- Demers Paradox
From: Aatu Koskensilta on 5 Jul 2010 09:40
Charlie-Boo <shymathguy(a)gmail.com> writes: > And the proof that it can't be carried out in PA? How would you express Borel determinacy in the first-order language of arithmetic? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |