Abstract
Let B be a complete Boolean algebra. Scott and Solovay constructed a B -valued model of set theory V ( B ) ; in this paper a category-theoretic translation of V ( B ) is given, in the form of a B -valued model of category theory. The usual category-theoetic translation of V ( B ) , namely the category of sheaves Shv( B ), appears as an image of the B -valued model. The B -valued model lives in a category MOD( B ), which is intended to be the category of all B -valued models. The last part of the paper investigates Easton's construction, which is the construction of V ( B ) for a ‘large’ B . The construction (in MOD( B )) of the B -valued model of category theory can still be carried out in this case, though the construction of Shv( B ) fails.
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