Let κ be an arbitrary regular infinite cardinal and let C denote the set of κ-maximal cofinitary groups. We show that if GCH holds and C is a closed set of cardinals such that 1. κ ∈ C, ∀ν ∈ C(ν ≥ κ), 2. if |C| ≥ κ then [κ, |C|] ⊆ C, 3. ∀ν ∈ C(cof(ν) ≤ κ→ ν ∈ C), then there is a generic extension in which cofinalities have not been changed and such that C = {|G| : G ∈ C}. The theorem generalize...

We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof(κ) carries a partial square. A famous theorem in set theory is the result that the failure of the square principle κ, for a regular uncountable cardinal κ, is equiconsistent with a Mahlo cardinal. Solovay p...

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...