We consider generalizations of a well-known class of spaces, called by S. Mrówka, N ∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbersN . We denote these generalizations by ψ = ψ(κ,R) for κ ≥ ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R) \ ψ(ω,R)| = 1. In other words there is a unique free z-ultrafilt...

Let κ be a singular cardinal. Carol Karp’s notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf(κ). With a notion of satisfaction and (chain)-isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EFgame wh...

OBJECTIVE To evaluate radiologist agreement on the quantification of bronchiectasis by high-resolution computed tomography (HRCT). MATERIALS AND METHODS The HRCT scans of 43 patients with bronchiectasis were analyzed by two radiologists, who used a scoring system to grade the findings. Kappa (κ) values and overall agreement were calculated. RESULTS For the measurement and appearance of bron...

We transform the oscillator algebra with κ-deformed multiplication rule, proposed in [1, 2], into the oscillator algebra with κ-deformed flip operator and standard multiplication. We recall that the κ-multiplication of the κ-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with κ-multiplication and with κ-flip operation. On the...

OBJECTIVE Clinical examination of the knee is subject to measurement error. The aim of this analysis was to determine interobserver and intraobserver reliability of commonly used clinical tests in patients with knee osteoarthritis (OA). METHODS We studied subjects with symptomatic knee OA who were participants in an open-label clinical trial of intraarticular steroid therapy. Following standa...

Let κ < λ be regular cardinals. We say that an embedding j : V → M with critical point κ is λ-tall if λ < j(κ) and M is closed under κ-sequences in V . Silver showed that GCH can fail at a measurable cardinal κ, starting with κ being κ++-supercompact. Later, Woodin improved this result, starting from the optimal hypothesis of a κ++-tall measurable cardinal κ. Now more generally, suppose that κ ...

Suppose κ = cf(κ), λ > cf(λ) = κ and λ = λ. We prove that there exist a sequence 〈Bi : i < κ〉 of Boolean algebras and an ultrafilterD on κ so that λ = ∏ i<κ Depth(Bi)/D < Depth ( ∏ i<κ Bi/D) = λ . An identical result holds also for Length. The proof is carried in ZFC, and it holds even above large cardinals. 2010 Mathematics Subject Classification. Primary: 06E05, 03G05. Secondary: 03E45.