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Our main results are: (A) It is consistent relative to a large cardinal that holds but fails. (B) If holds and are two infinite cardinals such that and λ carries a good scale, then holds. (C) If are two cardinals such that κ is λ-Shelah and , then there is no good scale for λ.

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ(λ) to the set of all a with is not λ++-saturated (and even not -saturated in case 2λ = λ+). We actually prove the stronger result that there is with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ(λ) for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ(λ). We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to makes NGκ, λ λ+3-saturated.

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no (proper, fine, κ-complete) ideal on Pκ(λ) is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on Pκ(λ) that satisfy the square brackets partition relation , where μ is a cardinal ≥2. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ(λ) is strongly normal if and only if J+< (J+, μ)2 for every μ < κ, and we describe the least normal ideal J on Pκ(λ) such that J+ < (J+, κ)2.

Purpose Factors explaining recurrences of toxoplasmic retinochoroiditis (TRC) and their frequency are not understood. The aim of this study is to analyze their recurrence patterns, and search for an association with their clinical and biological features. Methods 40 consecutive cases of TRC with a positive aqueous humour (AH) tap for toxoplasmosis were retrospectively included. Inclusion criteria were: Goldman-Witmer coefficient (GWC)>2.0, positive immunoblot (IB) or positive PCR for Toxoplasma gondii. Further episodes, their characteristics, disease-free intervals, and treatments were collected. We performed a case-control analysis of patients with and without recurrences during follow-up. Results Mean age was 41.5 years. 10% of patients were immunodeficient (n=4). Mean follow-up was 7.3 years (5.8-10.3). Forty-three percent of patients (n=17) presented at least one recurrence, with a mean of 1.7 episodes (1-4) per patient. Mean interval between episodes was 27 months (3-73). For patients experiencing one recurrence or more, initial AH analysis showed a lower GWC, less additional bands on IB, and less positive PCRs, even though these trends did not reach statistical significance. Clinically, these patients had broader lesions, in more peripheral locations, and more intense vitritis than those with no recurrences. For the initial episode, durations of antibiotic and anti-inflammatory treatments were superior in the recurrence group. Sex, ethnicity, or immune status were not associated with a change in recurrence risk. Conclusion TRC recurrences seem to be influenced by clinical and biological features at baseline.