Using Koszmider’s strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ ≤ λ, κ = κ and 2 = κ, and η is an ordinal with κ ≤ η < κ and cf(η) = κ. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra B such that ht(B) = η + 1, wdα(B) = κ for every α < η and wdη(B) = λ (i.e. there is a local...

Let κ be a singular cardinal in V , and let W ⊇ V be a model such that κ+V = λ + W for some W -cardinal λ with W |= cf(κ) 6= cf(λ). We apply Shelah’s pcf theory to study this situation, and prove the following results. 1) W is not a κ+-c.c generic extension of V . 2) There is no “good scale for κ” in V , so in particular weak forms of square must fail at κ. 3) If V |= cf(κ) = א0 then V |= “κ is...

Objective(s): Small cell lung cancer (SCLC) is an aggressive neuroendocrine carcinoma, which accounts for 10-15% of pulmonary cancers and exhibits early metastatic spread. This study aimed to determine the added value of 18F-FDG PET/CT imaging in tumor, node, and metastasis (TNM) staging of SCLC, compared to the conventional computed tomography (CT) scan and its potential role as a prognosticat...

We show that for many pairs of infinite cardinals κ > μ+ > μ, (κ+, κ) (μ+, μ) is consistent relative to the consistency of a supercompact cardinal. We also show that it is consistent, relative to a huge cardinal that (κ+, κ) (μ+, μ) for every successor cardinal κ and every μ < κ, answering a question of Foreman.

f : ∪A → ρ is called a conflict free coloring of the set-system A (with ρ colors) if ∀A ∈ A ∃ ζ < ρ ( |A ∩ f−1{ζ}| = 1 ). The conflict free chromatic number χCF(A) of A is the smallest ρ for which A admits a conflict free coloring with ρ colors. A is a (λ, κ, μ)-system if |A| = λ, |A| = κ for all A ∈ A, and A is μ-almost disjoint, i.e. |A ∩ A′| < μ for distinct A,A′ ∈ A. Our aim here is to stud...

If κ is an infinite cardinal, a complete Boolean algebra B is called κ-supported if and only if for each sequence 〈bβ : β < κ〉 of elements of B there holds V α<κ W β>α bβ = W A∈[κ]κ V β∈A bβ. We consider the problem of the existence of a non-atomic complete Boolean algebra B which is h2(B)-supported, where h2(B) is the minimal cardinal κ such that B is not (κ, 2)-distributive.

In this note we sketch the proofs of two results in combinatorial set theory. The common theme of the results is singular cardinal combinatorics: they involve the interaction between forcing, large cardinals, PCF theory and versions of Jensen’s weak square principle. 1. Changing cofinality Our first result involves an old question about changes of cofinality. Suppose that V,W are inner models o...

The symbol (XI)κ (with κ ≥ ω) denotes the space XI := Πi∈I Xi with the κ-box topology; this has as base all sets of the form U = Πi∈I Ui with Ui open in Xi and with |{i ∈ I : Ui 6= Xi}| < κ. The symbols w, d and S denote respectively weight, density character, and Souslin number. Generalizing familiar, classical results, the authors show inter alia: Theorem 3.10(b). If κ ≤ α+, |I| = α and each ...

OBJECTIVES The objective was to describe the interobserver agreement between trained chart reviewers and physician reviewers in a multicenter retrospective chart review study of children with cervical spine injuries (CSIs). METHODS Medical records of children younger than 16 years old with cervical spine radiography from 17 Pediatric Emergency Care Applied Research Network (PECARN) hospitals ...

As in the paper, suppose that allies use a threshold strategy according to which ally i supports the ruler if her signal ki is below some threshold k , ki ≤ k , and she rebels if ki > k . Since the signal ki is distributed uniformly on the interval [κ t − ε, κ + ε], a threshold signal k implies the existence of a threshold regime strength κ such that a rebellion fails if κ ≤ κ and succeeds if κ...