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Re: [ontolog-forum] First-Order Semantics

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Sat, 16 Jun 2007 01:39:38 +0200
Message-id: <4673233A.4050906@xxxxxxxxxxx>
Christopher Menzel wrote:
>>> There are (as of course John and Pat know) 2^card(D) relations over
>>> any set (taking relations here to be sets of n-tuples).
>> Only if n=1.
> Only if D is finite.      (01)

My point was that a relation over a single set is a set of 1-tuples;
but see it as yet another example of my terminological pickyiness.    (02)

> The POINT, of course -- that D, no matter its  
> size, cannot contain all of the relations over D -- holds regardless.    (03)

Obviously.    (04)

> I must admit that, like any good platonist, I was thinking of D as  
> infinite, in which case what I say is true for all n.      (05)

A relation over an infinite set is still an (infinite) set of 1-tuples.
(But see above.)    (06)

> To cover the  
> general case of D any size, insert "at least" above after "There are".    (07)

At least, unless n=1.    (08)

vQ    (09)

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