Re: E! quantification and equivalence

On 1 Apr, 18:55, "mordov" <-knowled...@xxxxxxxxxx> wrote:
On Apr 1, 3:00 am, "un student" <un.stud...@xxxxxxxxx> wrote:

It is easy to translate "E!x : P(x)", meaning "there exists unique x
for which P(x)", to a sentence with only universal quantifier and
equality in FOL.

Is it possible to do that without equality? I would guess no but can't
construct a proof.

You can, provided the non-logical vocabulary is finite (i.e. there are
only finitely many predicate symbols).

Really? Suppose P is the only predicate symbol? How do you express
that there is a unique P without entity?

.

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