We prove that for any k≥3 each element of the h-quasiorder of finite k-labeled forests is definable in the ordinary first order language and, respectively, each element of the h-quasiorder of countable k-labeled forests is definable in the language Lω1ω, in both cases provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we characterize the automorphism groups of both structures and show that the structure of finite k-forests is atomic. Similar results hold true for two other relevant (...) structures: the h-quasiorder of finite k-labeled trees and of finite k-labeled trees with a fixed label of the root element. (shrink)

We consider fine hierarchies in recursion theory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness of fine hierarchies.

Russkai︠a︡ t︠erkovʹ i drugie statʹi -- V temnykh religioznykh luchakh.

The concept of activity focuses on the uniqueness of human social life, which consists of the fact that men purposively transform objective nature and social reality. The characteristic feature of the social life of human beings is that it is manifested only through their activity, which has various aspects and forms.

The subject matter of the article is a standard cosmological model of the Universe. Contemporary opinion regarding origin, structure, and evolution of the Universe is of great interest. The answer to the question of the Universe origin is given by the Big Bang Theory. Is it possible to be sure in this theory correctness, which persuading of the Universe origination from the singularity fluctuation, when the World had appeared from nowhere, that is from abstract nothingness, further accelerated expansion of the (...) Universe following the Big Bang, and its development up to present with inexplicable source of energy for that. However, in the extreme end of the meta-universe the speed of stellar formations runaway is about the light velocity. Further, there is a new problem, the finiteness of the Universe. There are two counter-opinions, if the expanding Universe is finite or infinite. A very important question arises here, the question regarding isolatedness of the Universe as a system. The problem of the Universe heat death is closely connected with it. For this reason it is the time to discuss the Universe entropy. There is a short description of notions and problems with reference to this branch of knowledge, as well as of Doppler and Ritz effects alongside with Habble Law. The authors’ detailed interpretation of an entropy is also suggested. The analysis of the existing model is followed by the idea of the authors about the Universe organization. The style of the article is popular-science. In the first part of the article the existing concept of the Expanding Universe Theory and the dynamical Friedmann-Lemaitre models are described; it deals with the existing concept of the Big Bang Theory as well as the dark energy and the dark matter notions. In the second part the author gives detailed interpretation of an entropy. In the last part the problem of theoretical basis and fact nonconformity within the Expanding Universe Model Theory and the authors’ idea about the Universe organization are considered. (shrink)

We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau’s theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.