There, they call arithmetic soundness what me (and many logician) call
soundness, when they refer to theories about numbers. Like Mendelson I
prefer to use the term logically valid, to what you call soundness.
I may have misstated myself, but the wiki article you pointed me to agrees
with
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Countably infinite does not mean recursively countably infinite.
This is something which I will explain in the seventh step thread.
There is theorem by Kleene which links Post-Turing degrees of
unsolvability with the shape of arithmetical
Le 12-juin-09, à 09:31, Bruno Marchal a écrit :
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Ah, that makes sense--I hadn't thought of combining multiple
universal quantifiers in that way, but obviously you can do so and
get a meaningful statement about arithmetic that for a
Le 12-juin-09, à 08:28, A. Wolf a écrit :
There, they call arithmetic soundness what me (and many logician)
call
soundness, when they refer to theories about numbers. Like
Mendelson I
prefer to use the term logically valid, to what you call soundness.
I may have misstated myself,
Logicians from different fields use terms in different ways. In
provability logic and in recursion theory, soundness means often
arithmetical soundness.
I understand.
Part of the reason for my particular viewpoint: there's a group of
professors at the college I work at who are working on
Jesse Mazer skrev:
Date: Wed, 10 Jun 2009 09:18:10 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Tue, 9 Jun 2009 18:38:23 +0200
From: tor...@dsv.su.se
To:
Date: Fri, 12 Jun 2009 18:40:14 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Wed, 10 Jun 2009 09:18:10 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Date: Fri, 12 Jun 2009 09:31:46 +0200
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Countably infinite does not mean recursively countably infinite. This is
something which I
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