In axiomatic quantum field theory, the postulate of uniqueness vacuum (a pure state) is independent from other axioms and equivalent to cluster decomposition property. The latter, however, implies a Coulomb or Yukawa attenuation interactions at growing distances hence cannot accommodate confining properties strong interaction. Thesolution Yang–Mills theory given previously uses an auxiliary inc...

Lecture 1, 07.03.: We made a review of the material covered in Chapter I of [3], up to Theorem I.9.11 (Transfinite Recursion on Well-founded Relations). Lecture 2, 14.03.: We discussed the notion of a rank, as well as the Mostowski collapsing function material corresponding to Section 9 of [3]. Lecture 3, 04.04.: We discussed hereditarily transitive sets, the DownwardLöwenheim-Skolem-Tarksi The...

Elementary set theory can be studied informally and intuitively, and so can be taught in primary schools using, say, Venn diagrams. The intuitive approach silently assumes that all objects in the universe of discourse satisfying any defining condition form a set. This assumption gives rise to antinomies, the simplest and best known of which being Russell's paradox. Axiomatic set theory was orig...

Everyone is aware that measurement is a cornerstone of science, one that in some cases is highly controversial. Much complex technology underlies the refined measurement of certain physical quantities, some of which can be< estimated to surprisingly large numbers of significant figures; one of the more ' elaborate businesses spawned by the social sciences, a business that affects all of our liv...