Our aim is to show the consistency of 2κ ≥ κ+θ, for any θ < κ starting with a singular cardinal κ of cofinality ω so that ∀n < ω∃α < κ(o(α) = α). Dropping cofinalities technics are used for this purpose. 1 א1-gap and infinite drops in cofinalities Let κ be a singular cardinal of cofinality ω such that for each γ < κ and n < ω there is α, γ < α < κ, such that o(α) = α. We fix a sequence of cardi...

Filling the Gaps MANY doctors pride themselves as being one of a team: or part of a comprehensive service, which will give the best attention to all the needs of the patient. The medical student or student nurse is trained to see team work in operation not only between the different specialists and between them and the various (so-called) "ancillary" services, but even with an increasing number...

For the one-dimensional Schrödinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case. H. Giacomini et A. Mou...

In [5] Todorčević shows that there is no Hausdorff gap (A,B) if A is analytic. In this note we extend the result by showing that the assertion “there is no Hausdorff gap (A,B) if A is coanalytic” is equivalent to “there is no Hausdorff gap (A,B) if A is Σ2”, and equivalent to ∀r (א L[r] 1 < א1). We also consider real-valued games corresponding to Hausdorff gaps, and show that ADR for pointclass...

Purpose – This paper aims to examine how both the amount and type of coursework impact students’ conceptualizations of sustainability. Previous research demonstrates that academic coursework influences students’ environmental attitudes, yet few studies have examined the impact of coursework on how students conceptualize “sustainability”. Design/methodology/approach – Data are examined from the ...