Re: definition of identity

On Jun 28, 2:46 pm, Ken Pledger <ken.pled...@xxxxxxxxxxxxx> wrote:
In article <1183056741.897349.58...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

Zaljo...@xxxxxxxxx wrote:
....
In second order logic one can use the following axiom to define
identity:

AxAy( x=y <-> AP(P(x)<->P(y)) )

How this is wrote in FOL?
....

You're quite right in seeing a difficulty. That's the reason for
using "first order logic with identity", in which identity is introduced
as a special predicate symbol with its own axioms.

I thought that identity '=' is a relation symbol.
we don't wright =(x,y) , we usually write x=y.


Ken Pledger.

What are these axioms. Can you write them, or at least point to me a
site on the web that illustrate them.

Zuhair

.

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