Translation:There are not many mayors in Sweden.
Yes there are still a few, at least Linköping has one: http://www.linkoping.se/Demokrati-politik/Kontakta-din-politiker/Borgmastare/
Well, "borgmästare" was abolished as a formal title in 1971. In a few municipalities the "ordförande i kommunfullmäktige" call themselves borgmästare because it sounds cooler, I guess, but that's their own invention. It doesn't have much to do with the previous role of a Swedish borgmästare. http://sv.wikipedia.org/wiki/Borgm%C3%A4stare_i_Sverige :)
Yes. My original point was only that formally we haven't had mayors in Sweden since 1971. In later years a handful of municipalities (out of 290) have started using the title again, as a synonym to actual formal titles, and without any legal basis. It's not illegal, of course; it would be equally fine to use the title Lord of Spaghetti, or whatever. But I think that within Sweden it can only cause confusion these days, and some would see use of the title as an expression of vanity or something. My calling myself emperor doesn't mean we suddenly have emperors in Sweden (or does it?).
I totally see your point, they probably shouldn't call themselves mayors. It'll mess things up for future historians. On the other hand they're probably enjoying themselves. This is what happens in language all the time, people just keep using it the way they want to, so it never stays stable. Sometimes it's easy to feel that language would be so much better without its users :D
"Borgmästare" is the Swedish word for "mayor".
We no longer have it as an official/formal position, although a few people have started calling themselves borgmästare again because it's more ego-stroking and better-sounding than their formal title kommunstyrelsens ordförande (or kommunfullmäktiges ordförande). And sometimes they use it when dealing with international contacts, because it makes things easier.