There Is Exactly One

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There is one creator (at least one, maybe more).

\hspace{3mm} ∃x Creator(x)

Ahura Mazda is the one and only creator.

\hspace{3mm} Creator(a) ∧ ∀x( Creator(x) → x=a )

All squares are broken.

\hspace{3mm} ∀x( Sqr(x) → Brkn(x) )

There is one and only one creator.

\hspace{3mm} ∃y( Creator(y) ∧ ∀x( Creator(x) → x=y ) )

\hspace{3mm} or:

\hspace{3mm} ∃y ∀x( Creator(x) ↔ x=y )

There is one creator (at least one, maybe more).

∃x Creator(x)

Ahura Mazda is the one and only creator.

∃y( Creator(a) ∧ ∀x( Creator(x) → x=a )

All squares are broken.

∀x( Sqr(x) → Brkn(x) )

There is one and only one creator.

∃y( Creator(y) ∧ ∀x( Creator(x) → x=y ) )

Look, two quantifiers. But not just two quantifiers, one is existential and the other is universal. Mixed quantifiers!

Here's another, shorter way of expressing the same proposition (these are logically equivalent)

or:

∃y( ∀x( Creator(x) ↔ x=y ) )

Ex: There is one and only one female creator.

Ex: There is one and only one creator and she is female.