This article is cited in 5 papers

Function Representation of the Boolean-Valued Universe

A. E. Gutman^a, G. A. Losenkov<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

Abstract: 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.

Key words: Boolean-valued analysis, function representation, Stone space, continuous bundle, continuous section.

UDC: 517.98

Received: 01.11.1997

 English version: Siberian Advances in Mathematics, 1998, 8:1, 99–120

Bibliographic databases:

• 
•