THE “NON-STANDARD” FORMALISM OF QUANTUM THEORY II: FUNDAMENTAL ROTATIONS, THE ORDINAL PARADIGM

This article is the second article in the series of “non-standard” formalism of quantum theory. It develops the set-theoretic paradigm and substantiates the notion of fundamental rotation, which was introduced at the intuitive level in the first article of the series. It is shown that the fundamental rotation is a carrier of an ordinal infinity. We prove a number of theorems on the relation between the carriers of ordinal and quantitative infinity in particular, we formulate the condition under which the carrier of infinity is a set. It is shown that for the set-theoretic continuum S ( N ) this condition is not fulfilled, and hence S ( N ), contrary to G. Cantor’s wish, is not a set. Due to the large amount of material, this article is the second part of the general article. It presents the key points of the set-theoretic paradigm, while the third part formulates and develops the ordinal paradigm.