For each mathematical statement, only finitely many of its generalizations are useful: a formal proof of E. Bishop's idea
Olga M. Kosheleva, Владик Крейнович · International Mathematical Forum · 2014
Copyright c ○ 2014 Olga Kosheleva and Vladik Kreinovich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Generalization is one of the main mathematical activities. Some generalizations turn out to be useful for working mathematics, while many other generalizations have so far been not very useful. E. Bishop believed that most fruitless-so-far generalizations are hopeless, that every mathematical statement has only a few useful generalizations. In this paper, we show that, under a natural definition of the notion of useful generalization, Bishop’s belief can be proven – moreover, it turns out that for each mathematical statement, only finitely many of its generalizations are useful.