Editorial decision.
There are four ways of writing the name of the
mathematician and the things named after him: Godel, Goedel, Gödel, and Gödel.
Unfortunately the E2 search and hardlink mechanism does not recognize o and ö as the same letter, and of course oe will not match either. And HTML entities like ö should never be used in node titles. So I have decided the best compromise is to use plain O, and move all relevant write-ups across to the plain-O title.
If in due course the search mechanism is improved, it will be possible to give Herr Gödel and all his works the umlaut they deserve.
-- Gritchka
Somewhat inconsistently, I have left the umlaut on the title of the famous book Gödel, Escher, Bach: An Eternal Golden Braid, because that book title is in English, and is a proper name. Whereas Kurt Godel's name is German, and there are different ways German accented names can be rendered in English. If you search for "godel escher bach" the findings will lead you to the book.