Stable embeddedness and NIP

We give sufficient conditions for a predicate P in a complete theory T to be stably embedded: P with its induced 0-definable structure has "finite rank", P has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson and Onshuus in the case where P is o-minimal in T.Comment: 10 page

Intakes, adequacy, food sources and biomarker status of iron, folate, and vitamin B₁₂ in Māori and non-Māori octogenarians : life and living in advanced age : a cohort study in New Zealand (LiLACS NZ) : a thesis presented in partial fulfilment of the requirements for the degree of Masters of Science in Nutrition and Dietetics, Massey University, Albany, New Zealand

Background: Iron, folate and vitamin B12 are the three key nutrients associated with the development of anaemia and have also been associated with the dietary patterns linked to higher malnutrition risk in older adults. Octogenarians may be at increased risk for iron, folate and vitamin B12 deficiency due to reduced food intake. Dietary factors, cooking methods, medications, presence of inflammation, and impaired gastrointestinal absorption may affect the availability and bioavailability of these nutrients. There are currently no specific nutrient reference values (NRVs) or biomarker cut-offs for adults in advanced age and little is known about the relationship between dietary intake and biomarkers for older adults. Aim: To investigate the intake, adequacy, food sources and biomarker status of iron, folate and vitamin B12 and the relationship between dietary intake and biomarkers. Methods: In the follow up assessment of LiLACS NZ, 216 Māori and 362 non-Māori participants completed a detailed dietary assessment using 2x 24-hr multiple pass recalls. Adequacy of iron, folate and vitamin B12 were determined by comparison to the Estimated Average Requirement (EAR) for adults aged 71+ years. Serum ferritin, serum iron, total iron binding capacity, transferrin saturation, red blood cell (RBC) folate, serum folate, serum vitamin B12 and haemoglobin were compared to recognised cut-offs for adults. Generalised linear models and binary regression estimated the association between dietary intake and biomarkers. Results: Most participants had adequate dietary iron intakes (88% Māori; 95% non-Māori above EAR) and biomarkers for iron (>94% above cut-offs). The EAR for vitamin B12 was met by 74% Māori; 78% non-Māori and folate met by 42% Māori; 49% non-Māori. Māori versus non-Māori had higher intakes of vitamin B12 (p=0.038) and serum vitamin B12 (p=0.026). Increased dietary folate intake was associated with increased RBC folate for Māori (p=0.001) and non-Māori (p=0.014) and with increased serum folate for Māori (p215μg/day was associated with reduced risk of deficiency in RBC folate for Māori (p=0.001). Conclusions: Dietary intake and stores of iron are largely adequate in this population. Strategies to optimise the intake and bioavailability of foods rich in folate and vitamin B12 may be beneficial

On the Generic Type of the Free Group

We answer a question raised by Pillay, that is whether the infinite weight of the generic type of the free group is witnessed in $F_{\omega}$. We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not $\aleph_1$-homogeneous.Comment: To appear in J. of Symbolic Logi