How Can ZFC/PA do much of Math - it Can't Even Prove PA is Consistent (EASY PROOF)
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From: Charlie-Boo on 3 Jul 2010 13:56 On Jul 3, 8:44 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(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. Good. Really. Most people here resort to personal attacks when all of their attempts to BS their way through a problem fail. Humor is much better. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Charlie-Boo on 3 Jul 2010 13:58 On Jul 3, 8:48 am, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > Charlie-Boo wrote: > > > On Jun 29, 10:16 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > > Ok. What is the reference to the proof in ZFC of PA consistency doing > > > > it that way? > > > > 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? > > Woosh. Here's the real woosh: Any idiot knows he's just playing stupid games. But notice how my debunking logic works even for completely nonsensical responses! C-B > -- > I can't go on, I'll go on.
From: Charlie-Boo on 3 Jul 2010 13:59 On Jul 3, 8:48 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(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. And you won't post it, alas, so people could quickly and easily see it and debunk it like the other BS references. C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: herbzet on 3 Jul 2010 14:04 "R. Srinivasan" wrote: > Fortunately for me, at least a few quantum physicists who matter were > interested in (a new interpretation of) quantum physics, and that is > why I got my work published. I am pleased for you. Congratulations! -- hz
From: Charlie-Boo on 3 Jul 2010 14:12
On Jul 3, 10:39 am, William Hale <h...(a)tulane.edu> wrote: > In article > <6edea512-8a83-4c88-834e-a4ab9f77e...(a)z8g2000yqz.googlegroups.com>, > > Charlie-Boo <shymath...(a)gmail.com> wrote: > > On Jun 29, 10:22 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > Charlie-Boo <shymath...(a)gmail.com> writes: > > > > What is that formal expression? > > > > To find out you need to read a logic book. > > > Then why don't you (anyone) name one that has it? You can't name a > > book that has the proof or even the theorem spelled out, and you can't > > give it yourself, or even an outline. Yet you claim it can be done. > > Is that Mathematics? I thought statements had to be proven in > > Mathematics. > > I thought outlines were given, but you then asked for more detail, even > going as far to ask for it to be written completely formal, starting > from the axioms of ZFC without using any previous theorems. So far I believe only one person has even listed some ZFC axioms that will supposedly be used. When I asked what they will be used for and how they are essential, why PA can't do it because of them (which must be so due to Godel's 2nd), I got nothing in return. An authentic, intelligent, productive, normal, sane discussion would go something like this: 1. Someone posts a summary - high level overall - that gives the proof and how ZFC will formalize it. The axioms needed and how they are needed. 2. Others can ask question, get clarification or more details. 3. The information flows back and forth, freely. And what do we see here? 1. BS references that have no ZFC in the proof. 2. An explanation that refers to some theorem without mention of ZFC. 3. Mention of ZFC with no proof or theorem. 4. "Read a logic book." 5. "Figure it out yourself." If there were such a proof, people could have given and discussed it in less time than has been spent on BS and sarcasm. But they haven't. What do you conclude? When I discuss my results, I give as much detail and answer as many questions as people want - sometimes for days. I have nothing to hide. C-B > > > > > > C-B > > > > It appears the generous > > > explanations various people have provided for your benefit in news are > > > not sufficient. > > > > -- > > > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > > > "Wovon man nicht sprechan kann, dar ber muss man schweigen" > > > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus- Hide quoted text - > > - Show quoted text - |