The extended plus-one hypothesis—A relative consistency result

The Extended plus - One Hypothesis — a Relative Consistency Result Theodore

The Relative Consistency Of

We prove the consistency result from the title. By forcing we construct a model of g = ℵ1, b = cf(Sym(ω)) = ℵ2. We recall the definitions of the three cardinal characteristics in the title and the abstract. We write A ⊆ * B if A \ B is finite. We write f ≤ * g if f, g ∈ ω ω and {n : f (n) > g(n)} is finite. Definition 0.1. (1) A subset G of [ω] ω is called groupwise dense if – for all B ∈ G, A ...

A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability

The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. A...

Repeat Consistency of a Result

We address the following issue: Suppose that we have taken a dataset consisting of a set of events. We do an analysis on this dataset, and obtain a result of interest. We then take the same dataset, and repeat the analysis, possibly with differences, to again obtain a result on the same matter of interest. How do we determine whether our two results are “consistent”? Let us first attempt to ens...

The trion : two electrons plus one hole versus one electron plus one exciton

We first show that, for problems dealing with trions, it is totally hopeless to use the standard many-body description in terms of electrons and holes and its associated Feynman diagrams. We then show how, by using the description of a trion as an electron interacting with an exciton, we can obtain the trion absorption through far simpler diagrams, written with electrons and excitons. These dia...