Boolean-Valued Analysis of Algebraic Systems

Abstract

In any Boolean-valued universe there are, in particular, sets of various structures: groups, rings, algebras, etc.. Applying the descent functor to algebraic systems in the Boolean-valued model singles out structures with new properties and results in discovering new facts about their structure and interrelations. Such a technique, called direct Boolean-valued interpretation, allows one to produce new theorems or, to be more exact, to extend the semantical volume of the theorems available by way of straightforward translating. The information arising in such a way, however, not always proves to be really new, expedient or interesting, so that the unsophisticated Boolean-valued interpretation sometimes becomes an aimless game.