Re: sentences with infinite models and equivalence relations


> 1) = would definitely be required in adding to T the condition that the
> domain is infinite as you write, i just don't know how to formalize and
> this is what i am stuck on.

"There is at least 1 individual, and there are at least 2
individuals, and there are at least 3 individuals, and..."

> so what if i kept the above
> sentence and added the following condition:

> forall(x)exists(y)(Exy & x != y)

This says that every equivalence class has at least two members, so
you just need to add the condition that every equivalence class has
at most two members.

Your earlier formula

~EzAxAy[Exy & Exz & Ezy & ~x=y & ~x=z & ~y=z)

is just a logical truth as it stands - you need to make a small
change.






.

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