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Re: Expressability in the notation of set theory

Newsgroups sci.logic
Date 2023-06-08 15:04 -0700
References (9 earlier) <1f0728e4-dc6a-4436-8f5d-9750558e92c2n@googlegroups.com> <e0622cbf-3dbc-4bea-92b1-88651e2d7229n@googlegroups.com> <4645fa8c-363f-469c-b17d-b16210c15133n@googlegroups.com> <b8e2b95b-0729-43ce-8522-339c789930d0n@googlegroups.com> <4b097fae-1c63-43bf-ae65-ae8c9abac4a0n@googlegroups.com>
Message-ID <d3c2c586-c8bd-4e41-892b-e61e4adc842dn@googlegroups.com> (permalink)
Subject Re: Expressability in the notation of set theory
From Mild Shock <bursejan@gmail.com>

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Credits for the Translation go to Mahesh Viswanathan:

Second Order Logic - Mahesh Viswanathan Fall 2018
https://courses.engr.illinois.edu/cs498mv/fa2018/SecondOrderLogic.pdf

You basically find the bounded quantifier ∀X(X ⊆ U => F) here:

Definition 3:
assigns to every k-ary relational variable X_k a relation α2(X_k) ⊆ [u(A)]^k

For monadic second order, you only need k=1. Although
his function signature for α2 isn't correctly written out, 
and thefore his subsequent Definition 4 is a little hoppy.

Your Terrence Tao nonsense is wrong because it has 
only one r, but he talks about two dependencies and
not only one dependency.

Do you need glasses like John Gabriel. You get the Drinker
Paradox wrong, now you get Terrence Tao wrong,
because you don't pay attention?

Dan Christensen schrieb am Donnerstag, 8. Juni 2023 um 23:57:34 UTC+2:
> On Thursday, June 8, 2023 at 5:45:19 PM UTC-4, Mild Shock wrote: 
> > The translation MSO to FOL uses ordinary set theory. 
> > Where do you see something that isn't ordinary set theory?
> If you want to use ordinary set, you should have no problem with with this formalization:
> ALL(a):[a in u => EXIST(b):[b in u & (a,b) in r]] 
> & ALL(x):ALL(y):[x in u & y in u => ALL(a):ALL(b):ALL(c):ALL(d):[(a,b,c,d) in q 
> <=> (a,b,c,d) in u4 & [a=x & b=y & (x,c) in r & (y,d) in r]]] 
> 
> where u4 = u*u*u*u (Cartesian product)
> 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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Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-07 20:25 -0700
  Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-07 22:11 -0700
    Re: Expressability in the notation of set theory Julio Di Egidio <julio@diegidio.name> - 2023-06-07 23:34 -0700
      Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 07:31 -0700
  Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 00:51 -0700
    Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 01:03 -0700
      Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 01:19 -0700
      Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 08:04 -0700
        Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 11:10 -0700
          Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 11:40 -0700
          Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 11:51 -0700
            Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 12:16 -0700
              Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 12:34 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 13:47 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 13:57 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 14:11 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 14:42 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 14:45 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 14:51 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 14:57 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 15:04 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 15:09 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 15:28 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 15:48 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-08 15:54 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 19:43 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 19:32 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 14:38 -0700
  Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 21:19 -0700
    Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 00:21 -0700
      Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 00:28 -0700
        Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 00:34 -0700
          Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 00:48 -0700
      Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-09 06:57 -0700
        Re: Expressability in the notation of set theory Mild Shock <janburse@fastmail.fm> - 2023-06-09 21:04 +0200
          Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-09 13:28 -0700
            Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 15:42 -0700
              Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 15:58 -0700
                Re: Expressability in the notation of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-10 13:36 -0700
              Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-09 18:17 -0700
              Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-09 18:20 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 04:30 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 04:46 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-10 10:52 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 11:06 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 11:11 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 11:17 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-12 00:37 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-12 00:38 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-12 07:22 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-12 08:17 -0700
                Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-10 11:21 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 11:27 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-10 15:10 -0700
                Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-11 02:02 -0700
    Re: Expressability in the notation of set theory Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-09 12:03 -0700
      Re: Expressability in the notation of set theory Mild Shock <janburse@fastmail.fm> - 2023-06-09 21:12 +0200
        Re: Expressability in the notation of set theory Mild Shock <janburse@fastmail.fm> - 2023-06-09 21:22 +0200
          Re: Expressability in the notation of set theory Mild Shock <bursejan@gmail.com> - 2023-06-09 12:33 -0700

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