Re: For All x
- From: MoeBlee <jazzmobe@xxxxxxxxxxx>
- Date: Tue, 3 Feb 2009 12:11:26 -0800 (PST)
On Feb 3, 7:40 am, apoorv <sudhir...@xxxxxxxxxxx> wrote:
Suppose we have a set theory with just one axiom:
Ez Ax ~x e z [i.e there is a null set 0]
Would every set that contains 0 be a domain for a model of this
theory?
A set alone is not a model of a theory whose language has a 2-place
predicate symbol. Rather, a set with a binary relation on that set is
needed to be a model for the language, and then that will be a model
of the theory iff all members of the theory are true in that model.
For example:
map 'A' to {0}.
map 'e' to {<0 0>}.
The universe of that model has 0 as a member, but EzAx ~xez is not
true in that model.
In particular, would the truth value of Ax x=0 depend on the pre-
selected domain?
With the standard interpretation of '=', "Ax x=0" is true in all and
only those models whose universe is a singleton.
MoeBlee
.
- References:
- For All x
- From: apoorv
- Re: For All x
- From: William Elliot
- Re: For All x
- From: apoorv
- For All x
- Prev by Date: Re: For All x
- Next by Date: Re: For All x
- Previous by thread: Re: For All x
- Next by thread: Re: For All x
- Index(es):
Relevant Pages
|
