Interpolation and implicit definability in extensions of the provability logic

The provability logic GL was in the field of interest of A.V. Kuznetsov, who had also formulated its intuitionistic analog—the intuitionistic provability logic—and investigated these two logics and their extensions. In the present paper, different versions of interpolation and of the Beth property in normal extensions of the provability logic GL are considered. It is proved that in a large class of extensions of GL (including all finite slice logics over GL) almost all versions of interpolation and of the Beth property are equivalent. It follows that in finite slice logics over GL the three versions CIP, IPD and IPR of the interpolation property are equivalent. Also they are equivalent to the Beth properties B1, PB1 and PB2

Serum nesfatin in overweight and obese children

BACKGROUND: Obesity is one of the most common children diseases. In present time it is being actively studied the natural hormones role in the pathogenesis of obesity. AIMS: To determine the relationship between serum nesfatin level with impaired lipid metabolism in school age children with overweight and obesity. MATERIALS AND METHODS: The study included children with overweight and obesity («case») and healthy children with normal body mass («control») aged 9 to 15 years. All children were determined by concentration in cholesterol blood and its factions, apoA-1, apoB. Enzyme-linked immunosorbent assay (Bio Human Nesfatin Enzyme Immunoassay Kit). RESULTS: Groups of patients with overweight and obesity (n = 53) and healthy children (n = 31) were comparable by age and sex. In obese children, a significant decrease in the level of nesfatin-1 was revealed compared with the group with normal body weight. In cases of children obesity there is a marked decrease in the concentration of nesfatin-1 in serum, especially expressed in the dyslipidemia presence. The nesfatin-1 level are negatively correlated to BMI and body fat content. CONCLUSIONS: The obtained data suggest that along with the known key role of nesfatin in the regulation of eating behavior and appetite, it also affects anthropometric indicators, primarily associated with the accumulation of excess fat mass. Based on the data obtained, nesfatin-1 should be considered as a possible marker for the development of obesity in children

Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics

We consider the families of propositional superintuitionistic logics (s.i.l.) and NE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig's interpolation property (CIP), the disjunction property (DP), the Beth property (BP), Hallden-completeness (HP) etc. have suitable properties of varieties as their images, and many natural algebraic properties are in accordance with natural properties of logics. For example, a s.i.l. L has CIP iff its associated variety V(L) has the amalgamation property (AP); L is Hallden-complete iff V(L) is generated by a subdirectly irreducible Heyting algebra. For any n.m.l. L, the amalgamation property of V(L) is equivalent to a weaker version of the interpolation property for L, and the super-amalgamation property is equivalent to CIP; L is Hallden-complete iff V(L) satisfies a strong version of the joint embedding property. Well-known relational Kripke semantics for the intuitionistic and modal logics seems to be a more natural interpretation than the algebraic one. The categories of Kripke frames may, in a sense, be considered as subcategories of varieties of Heyting or modal algebras. We discuss the question to what extent one may reduce problems on properties of logics to consideration of their semantic models

Features of the chemokine profile of blood plasma by neurotoxic complications of acute lymphoblastic leukemia in children: preliminary report

The article presents an assessment of the neurotoxicity of chemotherapy in children with acute lymphoblastic leukemia receiving specific treatment according to the protocols used in pediatric oncological practice. An analysis of the neurological state with the determination of the chemokine profile of blood plasma was performed in 21 children aged 3 to 17 at the Regional Children’s Clinical Hospital in Yekaterinburg and the Central Research Laboratory of the Ural State Medical University in 2019. In the study group of children, neurotoxic complications were recorded in 42.9% of cases. At the same time, the appearance of neurological symptoms in most patients (77.7%) was observed during co chemotherapy at the stages of reinduction during consolidating treatment with a predominant clinical picture of chemo-induced polyneuropathy. In a comparative analysis of the indicators of the chemokine profile in groups of children, depending on the formation of neurotoxic complications during chemotherapy, we selected the chemokines CXCL10 (IP-10) and CXCL12 (SDF-1α) as possible prognostic biomarkers of damage to the nervous system