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Forum index » Science and Technology » Math » Undergraduate
infinite schema. (logic)
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Alon
science forum beginner


Joined: 30 May 2005
Posts: 5

PostPosted: Sun Jun 18, 2006 1:34 pm    Post subject: infinite schema. (logic) Reply with quote

is there a general way to prove that a wff is satisfiable by every infinite domian but not by finite domain?
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David C. Ullrich
science forum Guru


Joined: 28 Apr 2005
Posts: 2250

PostPosted: Mon Jun 19, 2006 11:45 am    Post subject: Re: infinite schema. (logic) Reply with quote

On Sun, 18 Jun 2006 09:34:50 EDT, Alon <alon_brookray@walla.com>
wrote:

Quote:
is there a general way to prove that a wff is satisfiable by every infinite domian but not by finite domain?

I think you need to rephrase the question slightly - I can't figure
out exactly what it means for a wff to be "satisfiable" in a given
domain.

There are certainly wffs that have infinite models but no
finite models, for example a wff that "says" that R(x,y)
is a linear order with no largest element. (Of course
that wff is not true in every infinite domain - hence
my confusion about "satisfiable in every infinite domain".)

************************

David C. Ullrich
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Alon
science forum beginner


Joined: 30 May 2005
Posts: 5

PostPosted: Mon Jun 19, 2006 12:31 pm    Post subject: Re: infinite schema. (logic) Reply with quote

i mean that if you are given a specific wff, and you need to determine is it satisfiable in an infinite domain but not finite or is it satisfiable by a finite domain but not by an infinite domain, is there a general way to determine or you should evaluate every wff as specific cases?
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