Easton's Results Via Iterated Boolean-Valued Extensions

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Abstract
The purpose of this article is to show how the main result of Easton [1] can be obtained as a special case of a general theory, which was developed in [6], of Boolean-valued models of ZF when the Boolean algebra is a proper class in the ground model. Indeed [1] was the motivating example for [6], Thus the present article together with [6] contain a presentation of Easton's forcing argument in the context of Boolean-valued models. This presentation is not, however, an automatic translation of Easton's argument from the language of forcing to that of Boolean-valued models. In fact, we hope to illuminate the "black magic" referred to in Rosser [8, p. 169].

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