Jones was appointed chairman. The null article example has a similar quality to your mayor example. Note that both zero article and null article refer to something that is.

It may be worth noting that in commonwealth english, no full-stop is included for abbreviations that. I'm jonesing for a little ganja, mon i'm jonesing for a little soul food, brother (verb) jonesed; Joneses to have a strong desire or craving for something (merriam webster) where