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| From | Mostowski Collapse <janburse@fastmail.fm> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: What is the simplest way to learn model theory? |
| Date | 2023-04-08 19:29 +0200 |
| Message-ID | <u0s89u$32lnv$1@solani.org> (permalink) |
| References | (7 earlier) <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> <u0s6hd$1b3m5$1@dont-email.me> |
LoL, thumbs up for the NIX PIX.
Will we soon see this on brilliant.org?
Julio Di Egidio schrieb:
> On 08/04/2023 18:24, Julio Di Egidio wrote:
>> 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.
>
> I still haven't read the article. Meanwhile,
> here is an example of vacuous truth:
>
> ```coq
>
> Theorem _what_empty_ :
> forall (X Y : Type),
> ~ inhabited X -> (* X uninhabited *)
> (* forall (f : X -> Y), *) (* no need *)
> forall (x : X),
> False. (* whatever *)
> Proof.
> intros X Y NIX (*f*) x.
> assert (PIX : inhabited X)
> by apply (inhabits x).
> apply (NIX PIX). (* contradiction *)
> Qed.
>
> ```
>
> Julio
>
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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
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