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| Newsgroups | sci.logic |
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| Date | 2023-05-03 16:16 -0700 |
| References | <c100517c-4b7c-4e83-86ef-02ce3e336698n@googlegroups.com> |
| Message-ID | <876183de-e906-40cb-9a2a-4bcc45ded451n@googlegroups.com> (permalink) |
| Subject | Re: Smullyan's Proof of the Drinkers Principle V3 |
| From | Mostowski Collapse <bursejan@gmail.com> |
With SET SPACES you cannot prove your "junk theorem". /* Junk Theorem Currently Provable */ 28 ALL(s):[Set(s) => EXIST(a):~a e s] Rem DNeg, 27 http://www.dcproof.com/UniversalSet.htm if you for example replace Set(s) by s ∈ 𝒫(U). Then what would go through in Coq with properly typing would amount to. You need to type the existential quantifier: /* Junk Theorem Not Provable Anymore */ ALL(s):[s ∈ 𝒫(U) => EXIST(a):[U(a) & ~a e s]] The above is not provable anymore. Sets s from 𝒫(U) do not always have elements inside U that are outside these sets. This is because we have that U ∈ 𝒫(U), which then violates the above theorem. So the Junk Theorem is not anymore provable if you use properly SET SPACES as mathematicians do one way or the other in most math books. Just check out Terrence Tao what he writes. Or things like sigma spaces in probability theory etc.. etc..
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Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-03 16:16 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:19 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:27 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-04 20:32 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 12:15 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:33 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 16:50 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 16:54 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:09 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 17:12 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 22:34 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 03:35 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-05 14:37 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:09 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-06 03:43 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-06 10:29 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 02:41 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 06:59 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-07 08:31 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:19 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:34 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:41 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:47 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-07 20:48 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-07 11:51 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 05:36 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-08 07:22 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 14:34 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-11 16:10 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-11 17:00 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <janburse@fastmail.fm> - 2023-05-12 12:04 +0200
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-12 03:13 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-12 07:12 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-04 11:40 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:43 -0700
Re: Smullyan's Proof of the Drinkers Principle V3 Mostowski Collapse <bursejan@gmail.com> - 2023-05-04 11:49 -0700
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