Abstract
All the ordinary mathematical systems are constructed in terms of sets. If we wish to study the reasoning used in mathematics, our model of mathematics must include some form of set theory, for otherwise our study must be restrictive. For example, Elementary Group Theory formalises almost nothing of group theory. The pervasive role of set theory in mathematics implies that any reasonable model of set theory will in effect contain a model of all of mathematics (including the mathematics of this book).
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