Resumo Objetivo Traduzir e adaptar transculturalmente a escala espanhola de Avaliação Sociofamiliar em Idosos (Escala Gijón) para o contexto brasileiro. Métodos Procedimento metodológico adequação transcultural, com tradução (espanhol-português), retrotradução (português-espanhol), avaliação equivalências semântica, idiomática, experimental conceitual, pré-teste da versão brasileira uma amostra...

We show that if Part(κ, λ) holds for every λ ≥ κ, then κ is strongly compact. Let κ be a regular infinite cardinal, and let λ ≥ κ be a cardinal. Pκ(λ) denotes the set of all subsets of λ of size less than κ. Part(κ, λ) means that for every F : Pκ(λ) × Pκ(λ) → 2, there is a cofinal subset A of (Pκ(λ),⊆) such that F is constant on the set {(a, b) ∈ A × A : a ⊂ b}. This definition is due to Jech [...

For a cardinal κ and a model M of cardinality κ let No(M) denote the number of non-isomorphic models of cardinality κ which are L∞κ-equivalent to M. In [She82] Shelah established that when κ is a weakly compact cardinal and μ ≤ κ is a nonzero cardinal, there exists a model M of cardinality κ with No(M) = μ. We prove here that if κ is a weakly compact cardinal, the question of the possible value...

Given a cardinal κ ≤ c, a subset of the plane is said to be a κ-point set if and only it it meets every line in precisely κ many points. In response to a question of Cobb, we show that for all 2 ≤ κ, λ < c there exists a κ-point set which is homeomorphic to a λ-point set, and further, we also show that it is consistent with ZFC that for all 2 ≤ κ < c, there exists a κ-point set X such that for ...

Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, and δ is not δ+ supercompact} is unbounded in κ. If in addition λ is 2λ supercompact, then A2 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, and δ is δ+ supercompact} is unbounded in κ as well...

We analyze Loewner traces driven by functions asymptotic to κ √ 1− t. We prove a stability result when κ 6= 4 and show that κ = 4 can lead to non locally connected hulls. As a consequence, we obtain a driving term λ(t) so that the hulls driven by κλ(t) are generated by a continuous curve for all κ > 0 with κ 6= 4 but not when κ = 4, so that the space of driving terms with continuous traces is n...

We analyze the effect of singularizing cardinals on square properties. An old theorem of Dzamonja-Shelah/Gitik says that if you singularize an inaccessible cardinal while preserving its successor, then κ,ω holds in the bigger model. We extend this to the situation where a finite interval of cardinals above κ is collapsed. More precisely, we show that if V ⊂ W , κ is inaccessible in V , cf (κ V ...

We give an application of our extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2 = κ together with 2 = λ for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible. When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2 = λ for all cardinals λ.

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(κ; ρ) is extended to the setting where the force points can be in the interior of the domain, radial SLE(κ) becomes chordal SLE(κ; ρ), with ρ = κ− 6, and vice versa. We also write down the martingales describing the Radon–Nykodim derivative of SLE(κ; ρ1, . . . , ρn) with...

By using combinatorial properties of stationary sets, we give a simple proof of some generalization of Silver’s Theorem i.e. if κ is an uncountable regular cardinal such that אκ is a singular strong limit cardinal, then the following hold. (1). If {α < κ : א<κ α ≤ אα·2} is stationary, then 2אκ ≤ אκ·2. (2). If {α < κ : א<κ α ≤ אα+γ}, where 0 < γ < κ, is stationary, then 2אκ ≤ אκ+γ.