Geodesic
Function Representation of the~Boolean-Valued Universe
Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 54-77.

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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. 
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     author = {A. E. Gutman and G. A. Losenkov},
     title = {Function {Representation} of {the~Boolean-Valued} {Universe}},
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A. E. Gutman; G. A. Losenkov. Function Representation of the~Boolean-Valued Universe. Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 54-77. http://geodesic.mathdoc.fr/item/MT_1998_1_1_a2/