In Michael Swan`s Practical English Usage I located today this sentence (so it`s no statement about me):
I`ve a good knowledge of English.
(As an example of a correct sentence, of course.)
I have always thought that the main verb to have (possessive sense) must not be shortened, only the auxiliary verb to have (I`ve always thought...) can. That`s why it should rather be like this:
I have a good knowledge of English.
What do you make of it?
Comp. Macmillan`s Dictionary for Advanced Learners, entry: have (red usage box p 654): "as a transitive verb used for talking about actions and experiences: ... Have got is not used, and neither short forms of have nor weak forms of pronunciation are ever used in these meanings ..."
(red usage box p. 656): The ordinary transitive uses of have are not usually shortened, though `ve and `d forms are sometimes possible:
It depends on dialect. To some native English speakers
I've a cat.
will sound awkward. To my knowledge, it's virtually impossible in America. People do however say such things in the UK.
I've no idea
is definitely not uncommon though.
The ordinary transitive uses of have are not usually`shortened, though ve and `d forms are sometimes possible.
This implies logically that if the transitive uses of have are not usually shortened, the shortened form is unusual and thus the exception. Being unusual is the very feature to define the term exception. Likewise, this conclusion is backed by the wording though ... are possible. The keyword here is though, which refers to the possibility of these forms inspite of the opposite rule.
Coming back to your point of departure: "I've some students who claim that. I've no idea who told them that..", I simply wonder why you can still not see why there are people like your students who take that well-founded position.
Dear birdeen`s call and thatone,
I have gratefully taken your points into consideration.
I have a cat.
I've got a cat.