Abstract
Abstract The theory of levels developed in Chapter 3 was wholly neutral as to how many levels there are in the hierarchy, since it was based solely on the axiom scheme of separation. Chapter 4 added the assumptions — the axioms of creation and infinity — which can be thought of as saying that the hierarchy extends to a certain height. But there are evidently other ways of extending the theory so as to assert that the hierarchy goes to other heights. Such assertions are called axioms of infinity. This chapter is concerned with whether there is a limit to the strength of axioms of infinity that are true and, if so, what it is.
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