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Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof. For the most part work in this field has remained close to foundational questions. Recent results, however, have indicated the possibility that the methods of mathematical logic may be of use in tackling specific problems in other branches of mathematics. This possibility is illustrated in the present paper, which presupposesdoi:10.1090/s0002-9947-1953-0055287-x fatcat:v4myi2s4pne6lg3j4vxj4x3iyi