Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
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 V31 (Semantically Incorrect Defined)
Date: Fri, 24 Jul 2020 20:20:10 +0100
Organization: A noiseless patient Spider
Lines: 28
Message-ID: <875zaclnyt.fsf@bsb.me.uk>
References: <Bf2dnacH3PC-wY7CnZ2dnUU7-VnNnZ2d@giganews.com> <871rl8dyg1.fsf@bsb.me.uk> <HvCdndl7NIZX64nCnZ2dnUU7-QXNnZ2d@giganews.com> <87lfjfovhm.fsf@bsb.me.uk> <qIidnXkfB8htv4jCnZ2dnUU7-YHNnZ2d@giganews.com> <87zh7tok63.fsf@bsb.me.uk> <6MednYs8F9v7qYvCnZ2dnUU7-R3NnZ2d@giganews.com> <87lfjcmg9p.fsf@bsb.me.uk> <ntCdnWze3_XLxYXCnZ2dnUU7-QvNnZ2d@giganews.com> <87tuxzkswv.fsf@bsb.me.uk> <yrCdnd_a1ILl3ofCnZ2dnUU7-dHNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain
Injection-Info: reader02.eternal-september.org; posting-host="3222cc71d7fcc6383df4f57f8b1050ad"; logging-data="13618"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/iL2lljzLY0tj6GVnE75nFjq7yKsUEk5Q="
Cancel-Lock: sha1:P7x0ZAKJTEOtMLm2XvJkmIx20WU= sha1:QjvSI76lo/xta8l72c4FZdARkl0=
X-BSB-Auth: 1.4f4290b1d3741816fc34.20200724202010BST.875zaclnyt.fsf@bsb.me.uk
Xref: csiph.com comp.theory:21886

olcott <NoOne@NoWhere.com> writes:

> OK great I carefully studied that part and totally understand it.

Can you give a language for Q yet?  You've moved on to interpretations,
but I'm not sure you know what a language is in this context.

> When
> we get to the next part where a denumerable sequence (s1,s2,s3,...) is
> said to satisfy a two place predicate, I don't get it. If you need an
> ordered pair to satisfy a relation then you really need a set of
> ordered pairs not a set of elements.

I see another, longer, reply.  I'll save any explanation for that post
but I will note that your language here is very sloppy.  Pairs can be
elements, so your "you need pairs not elements" dichotomy is false.
And, anyway, you need sequences or tuples (something ordered) to specify
an assignment to free variables, not sets.  It's no good saying that {2,
1, 3} satisfies x+y=z.  You need to be able to say that (1, 2, 3) and
(2, 1, 3) do but (3, 1, 2), (1, 3, 2), (3, 2, 1) and (2, 3, 1) don't.

(Don't let this example confuse you.  Mendelson does it slightly
differently for purely technical reasons.  The effect is the same.)

> I will keep rereading this page a few more times.

-- 
Ben.