Rogers semilattices of families of two embedded sets in the Ershov hierarchy

Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, the Rogers semilattice of the family is in nite. This condition is satis ed by every notation of !; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satis es this condition. On the other hand, we also give a su cient condition on a, that yields that there is a 1 a {computable family of two embedded sets, whose Rogers semilattice consists of exactly one element; this condition is satis ed by all notations of every successor ordinal bigger than 1, and by all notations of the ordinal !+!; moreover every computable ordinal that is sum of two smaller ordinals has a notation that satis es this condition. We also show that for every nonzero n 2 !, or n = !, and every notation of a nonzero ordinal there exists a 1 a {computable family of cardinality n, whose Rogers semilattice consists of exactly one element

Rogers semilattices of families of two embedded sets in the Ershov hierarchy

Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, the Rogers semilattice of the family is in nite. This condition is satis ed by every notation of !; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satis es this condition. On the other hand, we also give a su cient condition on a, that yields that there is a 1 a {computable family of two embedded sets, whose Rogers semilattice consists of exactly one element; this condition is satis ed by all notations of every successor ordinal bigger than 1, and by all notations of the ordinal !+!; moreover every computable ordinal that is sum of two smaller ordinals has a notation that satis es this condition. We also show that for every nonzero n 2 !, or n = !, and every notation of a nonzero ordinal there exists a 1 a {computable family of cardinality n, whose Rogers semilattice consists of exactly one element

Friedberg numberings in the Ershov hierarchy

We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice

Inductive inference and computable numberings

AbstractIt has been previously observed that for many TxtEx-learnable computable families of computably enumerable (c.e. for short) sets all their computable numberings are evidently 0′-equivalent, i.e. are equivalent with respect to reductions computable in the halting problem. We show that this holds for all TxtEx-learnable computable families of c.e. sets, and prove that, in general, the converse is not true. In fact there is a computable family A of c.e. sets such that all computable numberings of A are computably equivalent and A is not TxtEx-learnable. Moreover, we construct a computable family of c.e. sets which is not TxtBC-learnable though all of its computable numberings are 0′-equivalent. We also give a natural example of a computable TxtBC-learnable family of c.e. sets which possesses non-0′-equivalent computable numberings. So, for the computable families of c.e. sets, the properties of TxtBC-learnability and 0′-equivalence of all computable numberings are independent

National arts and crafts in the content of art education of Russia

© 2015, Canadian Center of Science and Education. All rights reserved. Main objective of this work is orientation of pedagogical thought to system use of an art material of the Russian national arts and crafts and, as a result, construction on the basis of it flexible educational technologies in the field of visual art at school. In particular, in article is opened value of studying of national arts and crafts in a context of formation of art culture of youth, conditions of integration of an art material of folk art in process of learning of fine art. Also in article are designated approaches in respect of definition of conditions of integration of a plastic and figurative material of folk art in the content of art education at school (national and regional, historical and art criticism and design). There is proved relevance of idea of synthesis of the national and applied and realistic fine arts in educational process. And, at last, is opened educational potential and prospects of folk art in creation of the content of learning in the sphere of art education

Medical examination of the adult population as a method of disease prevention

The article considers one of the main preventive methods used to prevent diseases and identify risk factors for diseases that are the main cause of death of the population – medical examination.В статье рассмотрен один из основных профилактических методов, применяемых для предупреждения заболеваний и выявления факторов риска заболеваний, являющихся основной причиной смертности населения, — диспансеризация

Market analysis of telemedicine services

The article provides an analysis of telemedicine services over the past two years in the healthcare sector. Currently, e-health technologies are being actively introduced in most countries of the world, one of the global directions of which is telemedicine.В статье приведен анализ телемедицинских услуг за последние два года в сфере Здравоохранения. В настоящее время в большинстве стран мира активно внедряются технологии электронного здравоохранения, одним из глобальных направлений которого является телемедицина