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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Simply defining =?iso-8859-1?Q?G=F6del?= Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability)
Date: Wed, 29 Jul 2020 22:47:52 +0100
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David Kleinecke <dkleinecke@gmail.com> writes:

> On Wednesday, July 29, 2020 at 11:31:27 AM UTC-7, olcott wrote:
<cut>
>> ∃!a26 ∈ humans ∃!a87 ∈ humans (Boolean Father_of(a26, a87))
>> 
>> Aside from the hand waving implied meaning of the "father of" relation 
>> that above is complete and correct.
>
> There is a set called H and a set of ordered triples <x, y, z>
> such that x and y belong to H and z belongs to Boolean (assumed
> known). Moreover there is a triple in the set for every x in H.
>
> But that is a clumsy way to state the matter.

And inadequate.  To make it look a bit like a relation you must exclude
both <x, y, T> and <x, y, F> from being present.

> Better would be:
>
>    There is a set called H and a function called F on H to H

That would make it a function and not a relation.  I don't see that as
better (PO is already confused.)

Better would be to stick to the usual definition of a binary relation on
H which is simply a subset of HxH.

> PS: This depends on a bit of jargon. As I use the terms "on H"
> means every member of H is involved.

-- 
Ben.