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Re: Smullyan's Proof of the Drinkers Principle V3

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Actually there is a class of proofs that fit this schema:

"Just tell me the theorem and a link to a normal (non-ZFC) proof 
and I will make a milestone for it and release it when you supply 
a link to a proof of it using only ZFC."
https://www.freelancer.com/projects/mathematics/Find-Common-Math-Theorem-Proven/ 

Sometimes a second order logic theorem can be translated
into a first order logic theorem with a little ZFC. A large class
of theorems that are in second order logic, are theorems

from second-order arithmetic. Second-order arithmetic is
also the main subject of reverse mathematics. There is also
a related model theory for certain subsystems:

The term was introduced by Mostowski (1959) as a 
strengthening of the notion of ω-model.
https://en.wikipedia.org/wiki/Beta-model

Guess what the two sorts of second 
order will be model theoretically?

Mild Shock schrieb am Mittwoch, 7. Juni 2023 um 22:31:17 UTC+2:
> About this competition by CeBo: 
> https://www.freelancer.com/projects/mathematics/Find-Common-Math-Theorem-Proven/ 
> 
> You can prove the Drinker Paradox, a set theoretic version of, with 
> with very little of ZFC. Would this qualify for this competition? 
> 
> I would reveal one of the best kept secrets, even not known to 
> man, last to speak for Dan Christensen, and his DC Poop.
> Dan Christensen schrieb am Dienstag, 6. Juni 2023 um 19:13:23 UTC+2: 
> > (Correction) 
> > On Tuesday, June 6, 2023 at 1:40:51 AM UTC-4, Mild Shock wrote: 
> > > Its not that difficult to correctly translate second order logic 
> > > to first order logic. 
> > [snip] 
> > 
> > I see the need to quantify over sets and functions as in DC Proof and most advanced math textbooks. (Some say, that in itself is SOL.) However, I haven't come across any pressing need to quantify over logical propositions OR PREDICATES. I think it would only lead to confusion. Thanks anyway. 
> > Dan 
> > 
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com 
> > Visit my Math Blog at http://www.dcproof.wordpress.com

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Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 08:53 -0700
  Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 08:56 -0700
    Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:03 -0700
      Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 09:34 -0700
        Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:38 -0700
          Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 09:39 -0700
            Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 10:24 -0700
              Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <janburse@fastmail.fm> - 2023-05-29 19:49 +0200
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 11:10 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 13:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 13:58 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:17 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 15:24 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-29 17:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 18:52 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:04 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-29 19:34 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-05-30 15:18 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 11:39 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 15:56 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:53 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:40 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:48 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-05 22:57 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 07:37 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-06 09:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 10:13 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:31 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:37 -0700
                Re: Smullyan's Proof of the Drinkers Principle V3 Mild Shock <bursejan@gmail.com> - 2023-06-07 13:42 -0700

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