Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅ there are differences. Our main result is a structure theory for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k.

We continue exploring analogues of o-minimality and weak o-minimality for circularly ordered sets. The main result is a description of ℵ0-categorical 1-transitive non-primitive weakly circularly minimal structures of convexity rank 1 up to binarity.

Here we study properties of weakly circularly minimal cyclically ordered groups. The main result of the paper is that any weakly circularly minimal cyclically ordered group is abelian.

The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature $\{ . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the Exchange (...) Principle for algebraic closure in a weakly o-minimal structure. (shrink)

Muslim women; religious life; Islmic call.

We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.

A law is one of the basic concepts of the dialectical materialist conception of determinism as a philosophical theory of the objective interrelationship and mutual conditioning of phenomena in the material and mental world. A law establishes a rigorously determined connection among circumstances, i.e., a totality of derivative components and conditions of their actions and results. By overlooking the existence of two different levels—the concept and the objective reality corresponding to it—some philosophers erroneously interpret Marx's theses concerning the approximateness of (...) the realization of the laws of society. Let us take, for example, Marx's thesis that "In general, in capitalist production general laws are realized in a very confused and approximate way, merely as a prevailing tendency, as a kind of average among constant fluctuations that is never solidly established."1 Some investigators see this as an objectively existing social law in itself, attributing to it an "inexactitude" of operation, variation, and approximation, instead of seeing it as a specific application of a particular law. They thus forget that Marx said, in the Foreword to the very first volume of Capital: "The question does not specifically have to do with a greater or lesser degree of development of the social antagonisms that derive from the natural laws of capitalist production, but rather lies in these laws themselves, these trends, which operate and are realized with iron necessity.". (shrink)