Is there a close analogy between "one and only one", used to mean exactly one (as in "there is one and only one object satisfying that condition" etc.), and "if and only if"? "If" and "Only if" can be used separately to denote sufficient and necessary conditions, but I'm not sure whether the constituent parts of "one and only one" can be considered in isolation.
I think it looks like you could interpret "there is one X satisfying condition Y" as "there is one or possibly more X satisfying condition Y", but I am not sure about the difference in interpretation between "there is only one X satisfying condition Y" and "there is one and only one X satisfying Y". Could "there is only one X satisfying condition Y" be interpreted as "there could be one X, but possibly none satisfying Y"? I would appreciate any ideas on this. Thanks