Suddenly it is time to say good bye to one of my PhD thesis heroes.
Schlagwort: Modelltheorie
42.
For example the field of real numbers forms a structure R whose elements are the real numbers, with signature consisting of the individual constant 0 to name the number zero, a 1-ary function symbol - for minus, and two 2-ary function symbols + and . for plus and times. At first sight we can't add a symbol to express 1/x, since all the named functions have to be defined on the whole domain of the structure, and there is no such real number as 1/0. But on second thoughts this is not a serious problem; any competent mathematician puts the condition ‘x is not zero’ before dividing by x, and so it never matters what the value of 1/0 is, and we can harmlessly take it to be 42. But most model theorists are uncomfortable with any kind of division by zero, so they stick with plus, times and minus.