From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: categories@mta.ca
Subject: Re: Realizibility and Partial Combinatory Algebras
Date: Thu, 6 Feb 2003 10:44:33 +0000 (GMT) [thread overview]
Message-ID: <Pine.LNX.3.96.1030206103607.30286C-100000@penguin.dpmms.cam.ac.uk> (raw)
In-Reply-To: <20030204022954.98645.qmail@web12202.mail.yahoo.com>
On Mon, 3 Feb 2003, Galchin Vasili wrote:
>
> Hello,
>
> I understand (to some degree) full combinatory algebra, but I don't
> understand the motivation behind the definition of a partial combinatory
> algebra. E.g. why do we have Sxy converges/is defined?
I'd like to know the answer to this too. Why does *everyone*, in writing
down the definition of a PCA, include the assumption that Sxy is always
defined? As far as I can see, the only answer is "because everyone else
does so"; the condition is never used in the construction of
realizability toposes, or in establishing any of their properties.
In every case where you need to know that a particular term Sab is
defined, it's easy to find a particular c such that Sabc is provably
defined.
Peter Johnstone
next prev parent reply other threads:[~2003-02-06 10:44 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-02-04 2:29 Galchin Vasili
2003-02-05 18:19 ` John Longley
2003-02-12 19:28 ` Thomas Streicher
2003-02-06 10:44 ` Prof. Peter Johnstone [this message]
2003-02-07 12:57 ` Peter Lietz
2003-02-07 15:26 ` John Longley
2003-02-07 9:57 jvoosten
2003-02-07 23:43 ` Prof. Peter Johnstone
2003-02-09 19:09 ` Peter Lietz
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