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Re: What is the simplest way to learn model theory?

Newsgroups	sci.logic
Date	2023-04-08 09:31 -0700
References	(6 earlier) <37f7181f-1adf-472e-8ef8-6d762e789befn@googlegroups.com> <8dcf3f3b-9f3d-4d8f-9586-c027bba0b2b6n@googlegroups.com> <u0s0tv$1a9m5$1@dont-email.me> <2a2c775d-e131-45ac-846f-2a2785e13edcn@googlegroups.com> <aa5140a5-eacb-4850-81bc-7f667edf779bn@googlegroups.com>
Message-ID	<a92d5bfb-e795-42f6-962e-aacbd55fc19dn@googlegroups.com> (permalink)
Subject	Re: What is the simplest way to learn model theory?
From	Mostowski Collapse <bursejan@gmail.com>

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Julio wrote:
> you must say "forall (x : A), x = x",

Agreed thats what Coq requires. But how do you translate
it to FOL? Do you claim this FOL translation of "if A is 
uninhabitated then ALL(x : A) [P(x)] is true" is wrong:

¬∃xAx → ∀x(Ax → Px) is valid.
https://www.umsu.de/trees/#~3~7xA(x)~5~6x(A(x)~5P(x))

Informally I didn't mention P(x) when I said ALL(x:A) is true.
But from the context, because I clarified it via P(x) and the 
above theorem, it should be clear what was meant?

Julio Di Egidio schrieb am Samstag, 8. April 2023 um 18:24:16 UTC+2:
> On Saturday, 8 April 2023 at 18:01:16 UTC+2, Mostowski Collapse wrote: 
> 
> > So what is written here (page 7) is wrong, or whats your claim?
> I was talking of the notion(s) of function, and I have shown some 
> theorems (in Coq), not made any claims. ("Doesn't hold unless" is 
> the same as "holds if and only if", and then we can even prove it).
> > (A function type whose parameter type is uninhabited has a 
> > value: the empty function.) 
> > <https://people.cs.kuleuven.be/~bart.jacobs/coq-essence.pdf>
> If he says so... I should read the article, carefully. 
> 
> Julio

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What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 00:50 -0500
  Re: What is the simplest way to learn model theory? Python <python@invalid.org> - 2023-04-07 10:40 +0200
    Re: What is the simplest way to learn model theory? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-07 09:32 -0700
      Re: What is the simplest way to learn model theory? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-04-07 13:10 -0700
      Re: What is the simplest way to learn model theory? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-07 21:56 +0100
        Re: What is the simplest way to learn model theory? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-07 18:06 -0700
          Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 20:30 -0500
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            Re: What is the simplest way to learn model theory? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 12:57 -0700
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        Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 23:25 -0500
          Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-08 00:59 -0700
            Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-08 01:07 -0700
              Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 06:02 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 16:36 +0200
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 17:23 +0200
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-08 09:01 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-08 09:09 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 09:21 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 09:24 -0700
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                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-08 09:36 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 18:59 +0200
                Re: What is the simplest way to learn model theory? Mostowski Collapse <janburse@fastmail.fm> - 2023-04-08 19:29 +0200
                Re: What is the simplest way to learn model theory? Mostowski Collapse <janburse@fastmail.fm> - 2023-04-08 19:50 +0200
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                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 02:44 -0700
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                Re: What is the simplest way to learn model theory? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-09 10:08 -0700
                Re: What is the simplest way to learn model theory? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-10 08:19 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 08:27 -0700
                Re: What is the simplest way to learn model theory? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-10 10:53 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 12:42 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 12:59 -0700
                Re: What is the simplest way to learn model theory? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-10 21:48 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 23:44 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 01:18 -0700
                Re: What is the simplest way to learn model theory? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-04-11 08:55 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 03:48 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 03:52 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 16:57 +0200
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 17:24 +0200
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 10:44 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 11:23 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 13:52 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 14:04 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 14:12 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 14:14 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 14:25 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 14:26 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 14:29 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 14:43 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 14:59 -0700
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                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 16:12 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 16:23 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 16:29 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 16:40 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 16:41 -0700
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                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 09:48 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-11 06:35 -0700
                Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 16:22 -0700
                Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-09 15:57 -0700
                Re: What is the simplest way to learn model theory? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-09 14:41 -0700
                Re: What is the simplest way to learn model theory? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-09 23:12 +0100
            Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-08 06:09 -0700
        Re: What is the simplest way to learn model theory? [function defined] olcott <polcott2@gmail.com> - 2023-04-08 11:47 -0500
        Re: What is the simplest way to learn model theory? [Ben Bacarisse] olcott <polcott2@gmail.com> - 2023-04-11 16:16 -0500
  Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 16:16 -0500
    Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-07 14:24 -0700
      Re: What is the simplest way to learn model theory? Mostowski Collapse <bursejan@gmail.com> - 2023-04-07 14:27 -0700
    Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 16:33 -0500
      Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-07 14:52 -0700
        Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 16:55 -0500
          Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-07 15:03 -0700
            Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 17:15 -0500
              Re: What is the simplest way to learn model theory? Julio Di Egidio <julio@diegidio.name> - 2023-04-07 15:21 -0700
            Re: What is the simplest way to learn model theory? olcott <polcott2@gmail.com> - 2023-04-07 17:29 -0500

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