I had better insert a spelling note here on Goedel's name. The German vowels A, O, and U have modified forms that are written with two dots over them. This modification is called an umlaut. However, my terminal does not handle overstrikes, so I fall back on typing the letter E after the vowel in question. This is an alternative spelling, and in fact the original spelling.
Many German nouns use an umlaut to form the plural.
In present-day English, a few nouns survive with a corresponding vowel shift that is called an ablaut. We write the plural as woman-women. It can be completely silent, or an obscure vowel. In writing there is no problem. But in speaking we notice that you cannot ablaut a schwa.