Axiomatic primary and tertiary decomposition theory

Axiomatic Method and Category Theory

Axiomatic Quantum Theory

The aim of the following lecture is to give some rough overview over most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory. Before specializing to ordinary Hilbert space quantum theory it will be explained why common sense reasoning cannot be applied naively and the pragmatic procedure (quantum reasoning) of getting a...

Axiomatic Set Theory

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...

Axiomatic set theory

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...

Axiomatic Measurement Theory 1

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...