@article { Gutman19971102, author = "Gutman A.E. and Losenkov G.A.", title = "Function representation of the Boolean-valued universe", journal = "Siberian Adv. Math.", year = "1998", volume = "8", number = "1", pages = "99--120", annote = "For an abstract Boolean-valued system, a function analog is proposed that is a model whose elements are functions and the basic logical operations are calculated ``pointwise.'' The new notion of continuous polyverse is introduced and studied which is a continuous bundle of models of set theory. It is shown that the class of continuous sections of a continuous polyverse is a Boolean-valued system satisfying all basic principles of Boolean-valued analysis and, conversely, every Boolean-valued algebraic system can be represented as the class of sections of a suitable continuous polyverse.", keywords = "Boolean-valued analysis, function representation, Stone space, continuous bundle, continuous section" }