how do express “multiple” in predicate logic?

Question

I hope you can give me some tips on how to translate part of the following sentence into predicate logic:

“No woman loves a man that loves multiple women”.

Which quantifier would you use to express the part “multiple”? It of course means “more than one”, so the existential quantifier (expressing: at least one) as such does not seem enough... Any ideas?

Thank you in advance for any help you can give me!

Answer 1

Rephrase that part as

There are two different women loved by the man

$\exists x\exists y:$ Woman$(x)\, \land\,$Woman$(y)\, \land\, \lnot(x=y)\,\land\,$Love$(m,x)\, \land\,$Love$(m, y)$