The sentence 'Claire is John's wife' could it be changed either in:
If you answer could you please also tell me why that is so, or quote some grammar reference? I would appreciate that very much as I think my students will ask me this difficult question and will want to know the details.
Wife is a countable noun (in this context), and thus requires a determiner. In "Claire is John's wife", the genitive/possessive John's is the determiner. If John has only one wife, and can only have one wife, then you would use the definite article. This is because the simple fact of being 'wife' to John means she is unique.
Claire is the wife of John.
However, if we use wife in the sense of being a role, as in the last sentence of the above paragraph, it no longer requires an article in all contexts:
I now pronounce you man and wife.
Claire is wife to John.
I never learned how to behave as wife and mother.
This sort of use is now a little old-fashioned, though.
