The Elimination of Atomic Cuts and the Semishortening Property for Gentzen's Sequent Calculus with Equality

We study various extensions of Gentzen's sequent calculus obtained by adding rules for equality. One of them is singled out as particularly natural and shown to satisfy full cut elimination, namely also atomic cuts can be eliminated. Furthermore we tell apart the extensions that satisfy full cut elimination from those that do not and establish a strengthened form of the nonlenghtening property of Lifschitz and Orevkov

Expressing Infinity without Foundation

The axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed

High-end normal adrenocorticotropic hormone and cortisol levels are associated with specific cardiovascular risk factors in pediatric obesity: a cross-sectional study.

BACKGROUND: The hypothalamic-pituitary-adrenal (HPA) axis, and in particular cortisol, has been reported to be involved in obesity-associated metabolic disturbances in adults and in selected populations of adolescents. The aim of this study was to investigate the association between morning adrenocorticotropic hormone (ACTH) and cortisol levels and cardiovascular risk factors in overweight or obese Caucasian children and adolescents. METHODS: This cross-sectional study of 450 obese children and adolescents (aged 4 to 18 years) was performed in a tertiary referral center. ACTH, cortisol, cardiovascular risk factors (fasting and post-challenge glucose, high-density lipoprotein (HDL)-cholesterol, low-density lipoprotein (LDL)-cholesterol, triglycerides, and hypertension) and insulin resistance were evaluated. All analyses were corrected for confounding factors (sex, age, puberty, body mass index), and odds ratios were determined. RESULTS: ACTH and cortisol levels were positively associated with systolic and diastolic blood pressure, triglycerides, fasting glucose and insulin resistance. Cortisol, but not ACTH, was also positively associated with LDL-cholesterol. When adjusted for confounding factors, an association between ACTH and 2 h post-oral glucose tolerance test glucose was revealed. After stratification according to cardiovascular risk factors and adjustment for possible confounding factors, ACTH levels were significantly higher in subjects with triglycerides 6590th percentile (P 5.92 pmol/l) and cortisol (>383.5 nmol/l) although within the normal range were associated with increases in cardiovascular risk factors in this population. CONCLUSIONS: In obese children and adolescents, high morning ACTH and cortisol levels are associated with cardiovascular risk factors. High ACTH levels are associated with high triglyceride levels and hyperglycemia, while high cortisol is associated with hypertension and high LDL-cholesterol. These specific relationships suggest complex mechanisms through which the HPA axis may contribute to metabolic impairments in obesity, and merit further investigations